id sid tid token lemma pos cord-209166-1drg5gzp 1 1 key key JJ cord-209166-1drg5gzp 1 2 : : : cord-209166-1drg5gzp 1 3 cord-209166 cord-209166 NNP cord-209166-1drg5gzp 1 4 - - HYPH cord-209166-1drg5gzp 1 5 1drg5gzp 1drg5gzp CD cord-209166-1drg5gzp 1 6 authors author NNS cord-209166-1drg5gzp 1 7 : : : cord-209166-1drg5gzp 1 8 Tah Tah NNP cord-209166-1drg5gzp 1 9 , , , cord-209166-1drg5gzp 1 10 Rajdeep Rajdeep NNP cord-209166-1drg5gzp 1 11 ; ; : cord-209166-1drg5gzp 1 12 Mazumdar Mazumdar NNP cord-209166-1drg5gzp 1 13 , , , cord-209166-1drg5gzp 1 14 Sarbajit Sarbajit NNP cord-209166-1drg5gzp 1 15 ; ; : cord-209166-1drg5gzp 1 16 Parida Parida NNP cord-209166-1drg5gzp 1 17 , , , cord-209166-1drg5gzp 1 18 Krishna Krishna NNP cord-209166-1drg5gzp 1 19 Kant Kant NNP cord-209166-1drg5gzp 2 1 title title NN cord-209166-1drg5gzp 2 2 : : : cord-209166-1drg5gzp 2 3 Study study NN cord-209166-1drg5gzp 2 4 of of IN cord-209166-1drg5gzp 2 5 the the DT cord-209166-1drg5gzp 2 6 Curvature curvature NN cord-209166-1drg5gzp 2 7 of of IN cord-209166-1drg5gzp 2 8 Liquid Liquid NNP cord-209166-1drg5gzp 2 9 Surface Surface NNP cord-209166-1drg5gzp 2 10 surrounding surround VBG cord-209166-1drg5gzp 2 11 a a DT cord-209166-1drg5gzp 2 12 Rotating rotate VBG cord-209166-1drg5gzp 2 13 Spherical spherical JJ cord-209166-1drg5gzp 2 14 Object object NN cord-209166-1drg5gzp 2 15 in in IN cord-209166-1drg5gzp 2 16 Gravity Gravity NNP cord-209166-1drg5gzp 2 17 Free Free NNP cord-209166-1drg5gzp 2 18 Space Space NNP cord-209166-1drg5gzp 2 19 date date NN cord-209166-1drg5gzp 2 20 : : : cord-209166-1drg5gzp 2 21 2020 2020 CD cord-209166-1drg5gzp 2 22 - - HYPH cord-209166-1drg5gzp 2 23 08 08 CD cord-209166-1drg5gzp 2 24 - - SYM cord-209166-1drg5gzp 2 25 26 26 CD cord-209166-1drg5gzp 2 26 journal journal NN cord-209166-1drg5gzp 2 27 : : : cord-209166-1drg5gzp 2 28 nan nan NNP cord-209166-1drg5gzp 2 29 DOI DOI NNP cord-209166-1drg5gzp 2 30 : : : cord-209166-1drg5gzp 2 31 nan nan NNP cord-209166-1drg5gzp 2 32 sha sha NNP cord-209166-1drg5gzp 2 33 : : : cord-209166-1drg5gzp 3 1 97b020f6e0ced2231e4ae144abf5d084756314a7 97b020f6e0ced2231e4ae144abf5d084756314a7 CD cord-209166-1drg5gzp 3 2 doc_id doc_id CD cord-209166-1drg5gzp 3 3 : : : cord-209166-1drg5gzp 4 1 209166 209166 CD cord-209166-1drg5gzp 4 2 cord_uid cord_uid NNS cord-209166-1drg5gzp 4 3 : : : cord-209166-1drg5gzp 5 1 1drg5gzp 1drg5gzp LS cord-209166-1drg5gzp 6 1 Concept concept NN cord-209166-1drg5gzp 6 2 of of IN cord-209166-1drg5gzp 6 3 curvature curvature NN cord-209166-1drg5gzp 6 4 of of IN cord-209166-1drg5gzp 6 5 liquid liquid NN cord-209166-1drg5gzp 6 6 surrounding surround VBG cord-209166-1drg5gzp 6 7 a a DT cord-209166-1drg5gzp 6 8 spherical spherical JJ cord-209166-1drg5gzp 6 9 surface surface NN cord-209166-1drg5gzp 6 10 seems seem VBZ cord-209166-1drg5gzp 6 11 obvious obvious JJ cord-209166-1drg5gzp 6 12 in in IN cord-209166-1drg5gzp 6 13 daily daily JJ cord-209166-1drg5gzp 6 14 life life NN cord-209166-1drg5gzp 6 15 , , , cord-209166-1drg5gzp 6 16 but but CC cord-209166-1drg5gzp 6 17 based base VBN cord-209166-1drg5gzp 6 18 on on IN cord-209166-1drg5gzp 6 19 earthly earthly JJ cord-209166-1drg5gzp 6 20 conditions condition NNS cord-209166-1drg5gzp 6 21 everywhere everywhere RB cord-209166-1drg5gzp 6 22 . . . cord-209166-1drg5gzp 7 1 However however RB cord-209166-1drg5gzp 7 2 , , , cord-209166-1drg5gzp 7 3 our -PRON- PRP$ cord-209166-1drg5gzp 7 4 understanding understanding NN cord-209166-1drg5gzp 7 5 about about IN cord-209166-1drg5gzp 7 6 the the DT cord-209166-1drg5gzp 7 7 concept concept NN cord-209166-1drg5gzp 7 8 seems seem VBZ cord-209166-1drg5gzp 7 9 more more RBR cord-209166-1drg5gzp 7 10 transparent transparent JJ cord-209166-1drg5gzp 7 11 when when WRB cord-209166-1drg5gzp 7 12 we -PRON- PRP cord-209166-1drg5gzp 7 13 keep keep VBP cord-209166-1drg5gzp 7 14 the the DT cord-209166-1drg5gzp 7 15 system system NN cord-209166-1drg5gzp 7 16 out out IN cord-209166-1drg5gzp 7 17 of of IN cord-209166-1drg5gzp 7 18 the the DT cord-209166-1drg5gzp 7 19 usual usual JJ cord-209166-1drg5gzp 7 20 earthly earthly JJ cord-209166-1drg5gzp 7 21 condition condition NN cord-209166-1drg5gzp 7 22 i.e. i.e. FW cord-209166-1drg5gzp 7 23 without without IN cord-209166-1drg5gzp 7 24 gravity gravity NN cord-209166-1drg5gzp 7 25 . . . cord-209166-1drg5gzp 8 1 Although although IN cord-209166-1drg5gzp 8 2 existence existence NN cord-209166-1drg5gzp 8 3 of of IN cord-209166-1drg5gzp 8 4 forces force NNS cord-209166-1drg5gzp 8 5 like like IN cord-209166-1drg5gzp 8 6 adhesion adhesion NN cord-209166-1drg5gzp 8 7 and and CC cord-209166-1drg5gzp 8 8 cohesion cohesion NN cord-209166-1drg5gzp 8 9 along along IN cord-209166-1drg5gzp 8 10 liquid liquid JJ cord-209166-1drg5gzp 8 11 surface surface NN cord-209166-1drg5gzp 8 12 come come VBP cord-209166-1drg5gzp 8 13 to to IN cord-209166-1drg5gzp 8 14 the the DT cord-209166-1drg5gzp 8 15 fore fore NN cord-209166-1drg5gzp 8 16 even even RB cord-209166-1drg5gzp 8 17 in in IN cord-209166-1drg5gzp 8 18 the the DT cord-209166-1drg5gzp 8 19 presence presence NN cord-209166-1drg5gzp 8 20 of of IN cord-209166-1drg5gzp 8 21 other other JJ cord-209166-1drg5gzp 8 22 force force NN cord-209166-1drg5gzp 8 23 like like IN cord-209166-1drg5gzp 8 24 gravitational gravitational JJ cord-209166-1drg5gzp 8 25 ones one NNS cord-209166-1drg5gzp 8 26 , , , cord-209166-1drg5gzp 8 27 but but CC cord-209166-1drg5gzp 8 28 without without IN cord-209166-1drg5gzp 8 29 gravity gravity NN cord-209166-1drg5gzp 8 30 these these DT cord-209166-1drg5gzp 8 31 forces force NNS cord-209166-1drg5gzp 8 32 are be VBP cord-209166-1drg5gzp 8 33 solely solely RB cord-209166-1drg5gzp 8 34 responsible responsible JJ cord-209166-1drg5gzp 8 35 for for IN cord-209166-1drg5gzp 8 36 kind kind RB cord-209166-1drg5gzp 8 37 of of RB cord-209166-1drg5gzp 8 38 observable observable JJ cord-209166-1drg5gzp 8 39 phenomenon phenomenon NN cord-209166-1drg5gzp 8 40 . . . cord-209166-1drg5gzp 9 1 Also also RB cord-209166-1drg5gzp 9 2 , , , cord-209166-1drg5gzp 9 3 we -PRON- PRP cord-209166-1drg5gzp 9 4 introduced introduce VBD cord-209166-1drg5gzp 9 5 a a DT cord-209166-1drg5gzp 9 6 form form NN cord-209166-1drg5gzp 9 7 of of IN cord-209166-1drg5gzp 9 8 force force NN cord-209166-1drg5gzp 9 9 responsible responsible JJ cord-209166-1drg5gzp 9 10 for for IN cord-209166-1drg5gzp 9 11 providing provide VBG cord-209166-1drg5gzp 9 12 a a DT cord-209166-1drg5gzp 9 13 form form NN cord-209166-1drg5gzp 9 14 of of IN cord-209166-1drg5gzp 9 15 potential potential JJ cord-209166-1drg5gzp 9 16 dominating dominate VBG cord-209166-1drg5gzp 9 17 over over IN cord-209166-1drg5gzp 9 18 the the DT cord-209166-1drg5gzp 9 19 gravitational gravitational JJ cord-209166-1drg5gzp 9 20 one one CD cord-209166-1drg5gzp 9 21 . . . cord-209166-1drg5gzp 10 1 The the DT cord-209166-1drg5gzp 10 2 discussion discussion NN cord-209166-1drg5gzp 10 3 was be VBD cord-209166-1drg5gzp 10 4 provided provide VBN cord-209166-1drg5gzp 10 5 an an DT cord-209166-1drg5gzp 10 6 ingenious ingenious JJ cord-209166-1drg5gzp 10 7 approach approach NN cord-209166-1drg5gzp 10 8 , , , cord-209166-1drg5gzp 10 9 by by IN cord-209166-1drg5gzp 10 10 conserving conserve VBG cord-209166-1drg5gzp 10 11 surface surface NN cord-209166-1drg5gzp 10 12 energy energy NN cord-209166-1drg5gzp 10 13 , , , cord-209166-1drg5gzp 10 14 it -PRON- PRP cord-209166-1drg5gzp 10 15 still still RB cord-209166-1drg5gzp 10 16 explains explain VBZ cord-209166-1drg5gzp 10 17 a a DT cord-209166-1drg5gzp 10 18 lot lot NN cord-209166-1drg5gzp 10 19 about about IN cord-209166-1drg5gzp 10 20 what what WP cord-209166-1drg5gzp 10 21 can can MD cord-209166-1drg5gzp 10 22 be be VB cord-209166-1drg5gzp 10 23 done do VBN cord-209166-1drg5gzp 10 24 more more JJR cord-209166-1drg5gzp 10 25 to to TO cord-209166-1drg5gzp 10 26 explore explore VB cord-209166-1drg5gzp 10 27 other other JJ cord-209166-1drg5gzp 10 28 properties property NNS cord-209166-1drg5gzp 10 29 of of IN cord-209166-1drg5gzp 10 30 rotating rotate VBG cord-209166-1drg5gzp 10 31 liquids liquid NNS cord-209166-1drg5gzp 10 32 in in IN cord-209166-1drg5gzp 10 33 free free JJ cord-209166-1drg5gzp 10 34 space space NN cord-209166-1drg5gzp 10 35 . . . cord-209166-1drg5gzp 11 1 Whenever whenever WRB cord-209166-1drg5gzp 11 2 we -PRON- PRP cord-209166-1drg5gzp 11 3 think think VBP cord-209166-1drg5gzp 11 4 of of IN cord-209166-1drg5gzp 11 5 Curvature curvature NN cord-209166-1drg5gzp 11 6 of of IN cord-209166-1drg5gzp 11 7 a a DT cord-209166-1drg5gzp 11 8 surface surface NN cord-209166-1drg5gzp 11 9 associated associate VBN cord-209166-1drg5gzp 11 10 to to IN cord-209166-1drg5gzp 11 11 a a DT cord-209166-1drg5gzp 11 12 system system NN cord-209166-1drg5gzp 11 13 , , , cord-209166-1drg5gzp 11 14 the the DT cord-209166-1drg5gzp 11 15 first first JJ cord-209166-1drg5gzp 11 16 thing thing NN cord-209166-1drg5gzp 11 17 which which WDT cord-209166-1drg5gzp 11 18 comes come VBZ cord-209166-1drg5gzp 11 19 to to IN cord-209166-1drg5gzp 11 20 our -PRON- PRP$ cord-209166-1drg5gzp 11 21 mind mind NN cord-209166-1drg5gzp 11 22 is be VBZ cord-209166-1drg5gzp 11 23 that that IN cord-209166-1drg5gzp 11 24 it -PRON- PRP cord-209166-1drg5gzp 11 25 is be VBZ cord-209166-1drg5gzp 11 26 related relate VBN cord-209166-1drg5gzp 11 27 to to IN cord-209166-1drg5gzp 11 28 the the DT cord-209166-1drg5gzp 11 29 profile profile NN cord-209166-1drg5gzp 11 30 of of IN cord-209166-1drg5gzp 11 31 the the DT cord-209166-1drg5gzp 11 32 surface surface NN cord-209166-1drg5gzp 11 33 i.e. i.e. FW cord-209166-1drg5gzp 11 34 the the DT cord-209166-1drg5gzp 11 35 physical physical JJ cord-209166-1drg5gzp 11 36 state state NN cord-209166-1drg5gzp 11 37 of of IN cord-209166-1drg5gzp 11 38 the the DT cord-209166-1drg5gzp 11 39 system system NN cord-209166-1drg5gzp 11 40 's 's POS cord-209166-1drg5gzp 11 41 surface surface NN cord-209166-1drg5gzp 11 42 . . . cord-209166-1drg5gzp 12 1 In in IN cord-209166-1drg5gzp 12 2 mathematical mathematical JJ cord-209166-1drg5gzp 12 3 sense sense NN cord-209166-1drg5gzp 12 4 , , , cord-209166-1drg5gzp 12 5 the the DT cord-209166-1drg5gzp 12 6 Curvature curvature NN cord-209166-1drg5gzp 12 7 is be VBZ cord-209166-1drg5gzp 12 8 defined define VBN cord-209166-1drg5gzp 12 9 as as IN cord-209166-1drg5gzp 12 10 the the DT cord-209166-1drg5gzp 12 11 amount amount NN cord-209166-1drg5gzp 12 12 by by IN cord-209166-1drg5gzp 12 13 which which WDT cord-209166-1drg5gzp 12 14 a a DT cord-209166-1drg5gzp 12 15 curve curve NN cord-209166-1drg5gzp 12 16 deviates deviate VBZ cord-209166-1drg5gzp 12 17 from from IN cord-209166-1drg5gzp 12 18 being be VBG cord-209166-1drg5gzp 12 19 a a DT cord-209166-1drg5gzp 12 20 straight straight JJ cord-209166-1drg5gzp 12 21 line line NN cord-209166-1drg5gzp 12 22 or or CC cord-209166-1drg5gzp 12 23 the the DT cord-209166-1drg5gzp 12 24 amount amount NN cord-209166-1drg5gzp 12 25 by by IN cord-209166-1drg5gzp 12 26 which which WDT cord-209166-1drg5gzp 12 27 a a DT cord-209166-1drg5gzp 12 28 surface surface NN cord-209166-1drg5gzp 12 29 deviates deviate VBZ cord-209166-1drg5gzp 12 30 from from IN cord-209166-1drg5gzp 12 31 being be VBG cord-209166-1drg5gzp 12 32 a a DT cord-209166-1drg5gzp 12 33 plane plane NN cord-209166-1drg5gzp 12 34 . . . cord-209166-1drg5gzp 13 1 The the DT cord-209166-1drg5gzp 13 2 Curvature curvature NN cord-209166-1drg5gzp 13 3 of of IN cord-209166-1drg5gzp 13 4 curves curve NNS cord-209166-1drg5gzp 13 5 drawn draw VBN cord-209166-1drg5gzp 13 6 on on IN cord-209166-1drg5gzp 13 7 a a DT cord-209166-1drg5gzp 13 8 surface surface NN cord-209166-1drg5gzp 13 9 is be VBZ cord-209166-1drg5gzp 13 10 the the DT cord-209166-1drg5gzp 13 11 main main JJ cord-209166-1drg5gzp 13 12 tool tool NN cord-209166-1drg5gzp 13 13 for for IN cord-209166-1drg5gzp 13 14 the the DT cord-209166-1drg5gzp 13 15 defining define VBG cord-209166-1drg5gzp 13 16 and and CC cord-209166-1drg5gzp 13 17 studying study VBG cord-209166-1drg5gzp 13 18 of of IN cord-209166-1drg5gzp 13 19 the the DT cord-209166-1drg5gzp 13 20 Curvature curvature NN cord-209166-1drg5gzp 13 21 of of IN cord-209166-1drg5gzp 13 22 the the DT cord-209166-1drg5gzp 13 23 surface surface NN cord-209166-1drg5gzp 13 24 . . . cord-209166-1drg5gzp 14 1 Now now RB cord-209166-1drg5gzp 14 2 , , , cord-209166-1drg5gzp 14 3 in in IN cord-209166-1drg5gzp 14 4 our -PRON- PRP$ cord-209166-1drg5gzp 14 5 case case NN cord-209166-1drg5gzp 14 6 we -PRON- PRP cord-209166-1drg5gzp 14 7 tend tend VBP cord-209166-1drg5gzp 14 8 to to TO cord-209166-1drg5gzp 14 9 study study VB cord-209166-1drg5gzp 14 10 the the DT cord-209166-1drg5gzp 14 11 Curvature curvature NN cord-209166-1drg5gzp 14 12 of of IN cord-209166-1drg5gzp 14 13 liquid liquid NN cord-209166-1drg5gzp 14 14 surrounding surround VBG cord-209166-1drg5gzp 14 15 a a DT cord-209166-1drg5gzp 14 16 spherical spherical JJ cord-209166-1drg5gzp 14 17 surface surface NN cord-209166-1drg5gzp 14 18 which which WDT cord-209166-1drg5gzp 14 19 is be VBZ cord-209166-1drg5gzp 14 20 in in IN cord-209166-1drg5gzp 14 21 - - HYPH cord-209166-1drg5gzp 14 22 turn turn NN cord-209166-1drg5gzp 14 23 rotating rotate VBG cord-209166-1drg5gzp 14 24 at at IN cord-209166-1drg5gzp 14 25 an an DT cord-209166-1drg5gzp 14 26 angular angular JJ cord-209166-1drg5gzp 14 27 velocity velocity NN cord-209166-1drg5gzp 14 28 ω ω NN cord-209166-1drg5gzp 15 1 but but CC cord-209166-1drg5gzp 15 2 in in IN cord-209166-1drg5gzp 15 3 the the DT cord-209166-1drg5gzp 15 4 absence absence NN cord-209166-1drg5gzp 15 5 of of IN cord-209166-1drg5gzp 15 6 a a DT cord-209166-1drg5gzp 15 7 major major JJ cord-209166-1drg5gzp 15 8 factor factor NN cord-209166-1drg5gzp 15 9 i.e. i.e. FW cord-209166-1drg5gzp 15 10 Gravity gravity NN cord-209166-1drg5gzp 15 11 . . . cord-209166-1drg5gzp 16 1 The the DT cord-209166-1drg5gzp 16 2 absence absence NN cord-209166-1drg5gzp 16 3 of of IN cord-209166-1drg5gzp 16 4 gravity gravity NN cord-209166-1drg5gzp 16 5 in in IN cord-209166-1drg5gzp 16 6 our -PRON- PRP$ cord-209166-1drg5gzp 16 7 case case NN cord-209166-1drg5gzp 16 8 is be VBZ cord-209166-1drg5gzp 16 9 a a DT cord-209166-1drg5gzp 16 10 key key JJ cord-209166-1drg5gzp 16 11 factor factor NN cord-209166-1drg5gzp 16 12 which which WDT cord-209166-1drg5gzp 16 13 helps help VBZ cord-209166-1drg5gzp 16 14 us -PRON- PRP cord-209166-1drg5gzp 16 15 to to TO cord-209166-1drg5gzp 16 16 study study VB cord-209166-1drg5gzp 16 17 our -PRON- PRP$ cord-209166-1drg5gzp 16 18 system system NN cord-209166-1drg5gzp 16 19 in in IN cord-209166-1drg5gzp 16 20 a a DT cord-209166-1drg5gzp 16 21 more more RBR cord-209166-1drg5gzp 16 22 transparent transparent JJ cord-209166-1drg5gzp 16 23 and and CC cord-209166-1drg5gzp 16 24 effective effective JJ cord-209166-1drg5gzp 16 25 way way NN cord-209166-1drg5gzp 16 26 i.e. i.e. FW cord-209166-1drg5gzp 16 27 it -PRON- PRP cord-209166-1drg5gzp 16 28 can can MD cord-209166-1drg5gzp 16 29 be be VB cord-209166-1drg5gzp 16 30 used use VBN cord-209166-1drg5gzp 16 31 to to TO cord-209166-1drg5gzp 16 32 study study VB cord-209166-1drg5gzp 16 33 the the DT cord-209166-1drg5gzp 16 34 Curvature curvature JJ cord-209166-1drg5gzp 16 35 properties property NNS cord-209166-1drg5gzp 16 36 of of IN cord-209166-1drg5gzp 16 37 fluids fluid NNS cord-209166-1drg5gzp 16 38 in in IN cord-209166-1drg5gzp 16 39 gravity gravity NN cord-209166-1drg5gzp 16 40 - - HYPH cord-209166-1drg5gzp 16 41 free free JJ cord-209166-1drg5gzp 16 42 space space NN cord-209166-1drg5gzp 16 43 . . . cord-209166-1drg5gzp 17 1 Although although IN cord-209166-1drg5gzp 17 2 we -PRON- PRP cord-209166-1drg5gzp 17 3 are be VBP cord-209166-1drg5gzp 17 4 neglecting neglect VBG cord-209166-1drg5gzp 17 5 Gravity gravity NN cord-209166-1drg5gzp 17 6 in in IN cord-209166-1drg5gzp 17 7 our -PRON- PRP$ cord-209166-1drg5gzp 17 8 system system NN cord-209166-1drg5gzp 17 9 , , , cord-209166-1drg5gzp 17 10 we -PRON- PRP cord-209166-1drg5gzp 17 11 will will MD cord-209166-1drg5gzp 17 12 still still RB cord-209166-1drg5gzp 17 13 consider consider VB cord-209166-1drg5gzp 17 14 the the DT cord-209166-1drg5gzp 17 15 existence existence NN cord-209166-1drg5gzp 17 16 of of IN cord-209166-1drg5gzp 17 17 other other JJ cord-209166-1drg5gzp 17 18 factors factor NNS cord-209166-1drg5gzp 17 19 ( ( -LRB- cord-209166-1drg5gzp 17 20 like like IN cord-209166-1drg5gzp 17 21 Cohesion cohesion NN cord-209166-1drg5gzp 17 22 forces force NNS cord-209166-1drg5gzp 17 23 ; ; : cord-209166-1drg5gzp 17 24 Adhesion adhesion NN cord-209166-1drg5gzp 17 25 forces force NNS cord-209166-1drg5gzp 17 26 ; ; : cord-209166-1drg5gzp 17 27 etc etc FW cord-209166-1drg5gzp 17 28 ) ) -RRB- cord-209166-1drg5gzp 17 29 which which WDT cord-209166-1drg5gzp 17 30 contribute contribute VBP cord-209166-1drg5gzp 17 31 for for IN cord-209166-1drg5gzp 17 32 the the DT cord-209166-1drg5gzp 17 33 change change NN cord-209166-1drg5gzp 17 34 in in IN cord-209166-1drg5gzp 17 35 the the DT cord-209166-1drg5gzp 17 36 Curvature curvature NN cord-209166-1drg5gzp 17 37 of of IN cord-209166-1drg5gzp 17 38 the the DT cord-209166-1drg5gzp 17 39 rotating rotate VBG cord-209166-1drg5gzp 17 40 system system NN cord-209166-1drg5gzp 17 41 's 's POS cord-209166-1drg5gzp 17 42 surface surface NN cord-209166-1drg5gzp 17 43 . . . cord-209166-1drg5gzp 18 1 In in IN cord-209166-1drg5gzp 18 2 the the DT cord-209166-1drg5gzp 18 3 absence absence NN cord-209166-1drg5gzp 18 4 of of IN cord-209166-1drg5gzp 18 5 gravity gravity NN cord-209166-1drg5gzp 18 6 , , , cord-209166-1drg5gzp 18 7 this this DT cord-209166-1drg5gzp 18 8 factors factor NNS cord-209166-1drg5gzp 18 9 will will MD cord-209166-1drg5gzp 18 10 be be VB cord-209166-1drg5gzp 18 11 solely solely RB cord-209166-1drg5gzp 18 12 responsible responsible JJ cord-209166-1drg5gzp 18 13 for for IN cord-209166-1drg5gzp 18 14 the the DT cord-209166-1drg5gzp 18 15 change change NN cord-209166-1drg5gzp 18 16 in in IN cord-209166-1drg5gzp 18 17 the the DT cord-209166-1drg5gzp 18 18 properties property NNS cord-209166-1drg5gzp 18 19 of of IN cord-209166-1drg5gzp 18 20 the the DT cord-209166-1drg5gzp 18 21 system system NN cord-209166-1drg5gzp 18 22 . . . cord-209166-1drg5gzp 19 1 Further further RB cord-209166-1drg5gzp 19 2 , , , cord-209166-1drg5gzp 19 3 we -PRON- PRP cord-209166-1drg5gzp 19 4 proceed proceed VBP cord-209166-1drg5gzp 19 5 to to TO cord-209166-1drg5gzp 19 6 calculate calculate VB cord-209166-1drg5gzp 19 7 the the DT cord-209166-1drg5gzp 19 8 restriction restriction NN cord-209166-1drg5gzp 19 9 on on IN cord-209166-1drg5gzp 19 10 the the DT cord-209166-1drg5gzp 19 11 angular angular JJ cord-209166-1drg5gzp 19 12 velocity velocity NN cord-209166-1drg5gzp 19 13 beyond beyond IN cord-209166-1drg5gzp 19 14 which which WDT cord-209166-1drg5gzp 19 15 the the DT cord-209166-1drg5gzp 19 16 centrifugal centrifugal JJ cord-209166-1drg5gzp 19 17 force force NN cord-209166-1drg5gzp 19 18 will will MD cord-209166-1drg5gzp 19 19 tend tend VB cord-209166-1drg5gzp 19 20 to to TO cord-209166-1drg5gzp 19 21 spill spill VB cord-209166-1drg5gzp 19 22 the the DT cord-209166-1drg5gzp 19 23 fluid fluid NN cord-209166-1drg5gzp 19 24 out out RP cord-209166-1drg5gzp 19 25 from from IN cord-209166-1drg5gzp 19 26 the the DT cord-209166-1drg5gzp 19 27 system system NN cord-209166-1drg5gzp 19 28 and and CC cord-209166-1drg5gzp 19 29 following follow VBG cord-209166-1drg5gzp 19 30 it -PRON- PRP cord-209166-1drg5gzp 19 31 , , , cord-209166-1drg5gzp 19 32 we -PRON- PRP cord-209166-1drg5gzp 19 33 will will MD cord-209166-1drg5gzp 19 34 try try VB cord-209166-1drg5gzp 19 35 to to TO cord-209166-1drg5gzp 19 36 study study VB cord-209166-1drg5gzp 19 37 the the DT cord-209166-1drg5gzp 19 38 various various JJ cord-209166-1drg5gzp 19 39 other other JJ cord-209166-1drg5gzp 19 40 properties property NNS cord-209166-1drg5gzp 19 41 of of IN cord-209166-1drg5gzp 19 42 the the DT cord-209166-1drg5gzp 19 43 system system NN cord-209166-1drg5gzp 19 44 by by IN cord-209166-1drg5gzp 19 45 conserving conserve VBG cord-209166-1drg5gzp 19 46 the the DT cord-209166-1drg5gzp 19 47 Surface Surface NNP cord-209166-1drg5gzp 19 48 Energy Energy NNP cord-209166-1drg5gzp 19 49 through through IN cord-209166-1drg5gzp 19 50 a a DT cord-209166-1drg5gzp 19 51 much much RB cord-209166-1drg5gzp 19 52 more more RBR cord-209166-1drg5gzp 19 53 ingenious ingenious JJ cord-209166-1drg5gzp 19 54 approach approach NN cord-209166-1drg5gzp 19 55 . . . cord-209166-1drg5gzp 20 1 In in IN cord-209166-1drg5gzp 20 2 Section section NN cord-209166-1drg5gzp 20 3 2 2 CD cord-209166-1drg5gzp 20 4 we -PRON- PRP cord-209166-1drg5gzp 20 5 will will MD cord-209166-1drg5gzp 20 6 describe describe VB cord-209166-1drg5gzp 20 7 our -PRON- PRP$ cord-209166-1drg5gzp 20 8 system system NN cord-209166-1drg5gzp 20 9 by by IN cord-209166-1drg5gzp 20 10 calculating calculate VBG cord-209166-1drg5gzp 20 11 the the DT cord-209166-1drg5gzp 20 12 Equatorial Equatorial NNP cord-209166-1drg5gzp 20 13 Bulge Bulge NNP cord-209166-1drg5gzp 20 14 ( ( -LRB- cord-209166-1drg5gzp 20 15 n n NN cord-209166-1drg5gzp 20 16 ) ) -RRB- cord-209166-1drg5gzp 20 17 and and CC cord-209166-1drg5gzp 20 18 also also RB cord-209166-1drg5gzp 20 19 by by IN cord-209166-1drg5gzp 20 20 deriving derive VBG cord-209166-1drg5gzp 20 21 the the DT cord-209166-1drg5gzp 20 22 Equation equation NN cord-209166-1drg5gzp 20 23 of of IN cord-209166-1drg5gzp 20 24 the the DT cord-209166-1drg5gzp 20 25 Spheroid spheroid NN cord-209166-1drg5gzp 20 26 formed form VBN cord-209166-1drg5gzp 20 27 by by IN cord-209166-1drg5gzp 20 28 the the DT cord-209166-1drg5gzp 20 29 fluid fluid NN cord-209166-1drg5gzp 20 30 due due IN cord-209166-1drg5gzp 20 31 to to IN cord-209166-1drg5gzp 20 32 the the DT cord-209166-1drg5gzp 20 33 rotation rotation NN cord-209166-1drg5gzp 20 34 of of IN cord-209166-1drg5gzp 20 35 the the DT cord-209166-1drg5gzp 20 36 system system NN cord-209166-1drg5gzp 20 37 . . . cord-209166-1drg5gzp 21 1 Then then RB cord-209166-1drg5gzp 21 2 in in IN cord-209166-1drg5gzp 21 3 Section section NN cord-209166-1drg5gzp 21 4 3 3 CD cord-209166-1drg5gzp 21 5 we -PRON- PRP cord-209166-1drg5gzp 21 6 will will MD cord-209166-1drg5gzp 21 7 derive derive VB cord-209166-1drg5gzp 21 8 the the DT cord-209166-1drg5gzp 21 9 expression expression NN cord-209166-1drg5gzp 21 10 for for IN cord-209166-1drg5gzp 21 11 the the DT cord-209166-1drg5gzp 21 12 Central Central NNP cord-209166-1drg5gzp 21 13 Fluid Fluid NNP cord-209166-1drg5gzp 21 14 Pressure Pressure NNP cord-209166-1drg5gzp 21 15 ( ( -LRB- cord-209166-1drg5gzp 21 16 P p NN cord-209166-1drg5gzp 21 17 0 0 CD cord-209166-1drg5gzp 21 18 ) ) -RRB- cord-209166-1drg5gzp 21 19 and and CC cord-209166-1drg5gzp 21 20 following follow VBG cord-209166-1drg5gzp 21 21 it -PRON- PRP cord-209166-1drg5gzp 21 22 we -PRON- PRP cord-209166-1drg5gzp 21 23 will will MD cord-209166-1drg5gzp 21 24 derive derive VB cord-209166-1drg5gzp 21 25 the the DT cord-209166-1drg5gzp 21 26 expression expression NN cord-209166-1drg5gzp 21 27 for for IN cord-209166-1drg5gzp 21 28 the the DT cord-209166-1drg5gzp 21 29 Containing Containing NNP cord-209166-1drg5gzp 21 30 Force Force NNP cord-209166-1drg5gzp 21 31 ( ( -LRB- cord-209166-1drg5gzp 21 32 F(x F(x NNP cord-209166-1drg5gzp 21 33 , , , cord-209166-1drg5gzp 21 34 y y NNP cord-209166-1drg5gzp 21 35 , , , cord-209166-1drg5gzp 21 36 z z NNP cord-209166-1drg5gzp 21 37 ) ) -RRB- cord-209166-1drg5gzp 21 38 ) ) -RRB- cord-209166-1drg5gzp 21 39 of of IN cord-209166-1drg5gzp 21 40 the the DT cord-209166-1drg5gzp 21 41 system system NN cord-209166-1drg5gzp 21 42 . . . cord-209166-1drg5gzp 22 1 After after IN cord-209166-1drg5gzp 22 2 deriving derive VBG cord-209166-1drg5gzp 22 3 both both CC cord-209166-1drg5gzp 22 4 the the DT cord-209166-1drg5gzp 22 5 previously previously RB cord-209166-1drg5gzp 22 6 mentioned mention VBN cord-209166-1drg5gzp 22 7 expressions expression NNS cord-209166-1drg5gzp 22 8 , , , cord-209166-1drg5gzp 22 9 we -PRON- PRP cord-209166-1drg5gzp 22 10 will will MD cord-209166-1drg5gzp 22 11 derive derive VB cord-209166-1drg5gzp 22 12 the the DT cord-209166-1drg5gzp 22 13 expression expression NN cord-209166-1drg5gzp 22 14 for for IN cord-209166-1drg5gzp 22 15 the the DT cord-209166-1drg5gzp 22 16 Angular Angular NNP cord-209166-1drg5gzp 22 17 Velocity Velocity NNP cord-209166-1drg5gzp 22 18 of of IN cord-209166-1drg5gzp 22 19 the the DT cord-209166-1drg5gzp 22 20 system system NN cord-209166-1drg5gzp 22 21 after after IN cord-209166-1drg5gzp 22 22 finding find VBG cord-209166-1drg5gzp 22 23 out out RP cord-209166-1drg5gzp 22 24 the the DT cord-209166-1drg5gzp 22 25 Moment moment NN cord-209166-1drg5gzp 22 26 of of IN cord-209166-1drg5gzp 22 27 Inertia Inertia NNP cord-209166-1drg5gzp 22 28 ( ( -LRB- cord-209166-1drg5gzp 22 29 I -PRON- PRP cord-209166-1drg5gzp 22 30 net net NN cord-209166-1drg5gzp 22 31 ) ) -RRB- cord-209166-1drg5gzp 22 32 and and CC cord-209166-1drg5gzp 22 33 Surface Surface NNP cord-209166-1drg5gzp 22 34 Area Area NNP cord-209166-1drg5gzp 22 35 ( ( -LRB- cord-209166-1drg5gzp 22 36 S S NNP cord-209166-1drg5gzp 22 37 ) ) -RRB- cord-209166-1drg5gzp 22 38 of of IN cord-209166-1drg5gzp 22 39 the the DT cord-209166-1drg5gzp 22 40 system system NN cord-209166-1drg5gzp 22 41 in in IN cord-209166-1drg5gzp 22 42 Section section NN cord-209166-1drg5gzp 22 43 4 4 CD cord-209166-1drg5gzp 22 44 . . . cord-209166-1drg5gzp 23 1 Then then RB cord-209166-1drg5gzp 23 2 in in IN cord-209166-1drg5gzp 23 3 Section section NN cord-209166-1drg5gzp 23 4 5 5 CD cord-209166-1drg5gzp 23 5 we -PRON- PRP cord-209166-1drg5gzp 23 6 will will MD cord-209166-1drg5gzp 23 7 find find VB cord-209166-1drg5gzp 23 8 the the DT cord-209166-1drg5gzp 23 9 expressions expression NNS cord-209166-1drg5gzp 23 10 for for IN cord-209166-1drg5gzp 23 11 the the DT cord-209166-1drg5gzp 23 12 Containing Containing NNP cord-209166-1drg5gzp 23 13 Force Force NNP cord-209166-1drg5gzp 23 14 ( ( -LRB- cord-209166-1drg5gzp 23 15 F(x F(x NNP cord-209166-1drg5gzp 23 16 ) ) -RRB- cord-209166-1drg5gzp 23 17 ) ) -RRB- cord-209166-1drg5gzp 23 18 along along IN cord-209166-1drg5gzp 23 19 X x NN cord-209166-1drg5gzp 23 20 - - NN cord-209166-1drg5gzp 23 21 axis axis NN cord-209166-1drg5gzp 23 22 , , , cord-209166-1drg5gzp 24 1 Limiting limit VBG cord-209166-1drg5gzp 24 2 ω ω CD cord-209166-1drg5gzp 24 3 and and CC cord-209166-1drg5gzp 24 4 the the DT cord-209166-1drg5gzp 24 5 Containing contain VBG cord-209166-1drg5gzp 24 6 Potential potential NN cord-209166-1drg5gzp 24 7 ( ( -LRB- cord-209166-1drg5gzp 24 8 Ψ(x Ψ(x NNP cord-209166-1drg5gzp 24 9 ) ) -RRB- cord-209166-1drg5gzp 24 10 ) ) -RRB- cord-209166-1drg5gzp 25 1 along along IN cord-209166-1drg5gzp 25 2 X x NN cord-209166-1drg5gzp 25 3 - - NN cord-209166-1drg5gzp 25 4 axis axis NN cord-209166-1drg5gzp 25 5 respectively respectively RB cord-209166-1drg5gzp 25 6 which which WDT cord-209166-1drg5gzp 25 7 we -PRON- PRP cord-209166-1drg5gzp 25 8 are be VBP cord-209166-1drg5gzp 25 9 accounting account VBG cord-209166-1drg5gzp 25 10 under under IN cord-209166-1drg5gzp 25 11 restricted restricted JJ cord-209166-1drg5gzp 25 12 conditions condition NNS cord-209166-1drg5gzp 25 13 . . . cord-209166-1drg5gzp 26 1 After after IN cord-209166-1drg5gzp 26 2 that that DT cord-209166-1drg5gzp 26 3 in in IN cord-209166-1drg5gzp 26 4 Section section NN cord-209166-1drg5gzp 26 5 6 6 CD cord-209166-1drg5gzp 26 6 we -PRON- PRP cord-209166-1drg5gzp 26 7 will will MD cord-209166-1drg5gzp 26 8 conclude conclude VB cord-209166-1drg5gzp 26 9 our -PRON- PRP$ cord-209166-1drg5gzp 26 10 results result NNS cord-209166-1drg5gzp 26 11 which which WDT cord-209166-1drg5gzp 26 12 we -PRON- PRP cord-209166-1drg5gzp 26 13 inferred infer VBD cord-209166-1drg5gzp 26 14 from from IN cord-209166-1drg5gzp 26 15 the the DT cord-209166-1drg5gzp 26 16 previous previous JJ cord-209166-1drg5gzp 26 17 sections section NNS cord-209166-1drg5gzp 26 18 using use VBG cord-209166-1drg5gzp 26 19 various various JJ cord-209166-1drg5gzp 26 20 concepts concept NNS cord-209166-1drg5gzp 26 21 followed follow VBN cord-209166-1drg5gzp 26 22 by by IN cord-209166-1drg5gzp 26 23 Acknowledgement Acknowledgement NNP cord-209166-1drg5gzp 26 24 in in IN cord-209166-1drg5gzp 26 25 Section Section NNP cord-209166-1drg5gzp 26 26 7 7 CD cord-209166-1drg5gzp 26 27 and and CC cord-209166-1drg5gzp 26 28 References reference NNS cord-209166-1drg5gzp 26 29 respectively respectively RB cord-209166-1drg5gzp 26 30 . . . cord-209166-1drg5gzp 27 1 We -PRON- PRP cord-209166-1drg5gzp 27 2 are be VBP cord-209166-1drg5gzp 27 3 considering consider VBG cord-209166-1drg5gzp 27 4 a a DT cord-209166-1drg5gzp 27 5 metal metal NN cord-209166-1drg5gzp 27 6 sphere sphere NN cord-209166-1drg5gzp 27 7 is be VBZ cord-209166-1drg5gzp 27 8 present present JJ cord-209166-1drg5gzp 27 9 in in IN cord-209166-1drg5gzp 27 10 free free JJ cord-209166-1drg5gzp 27 11 space space NN cord-209166-1drg5gzp 27 12 , , , cord-209166-1drg5gzp 27 13 with with IN cord-209166-1drg5gzp 27 14 no no DT cord-209166-1drg5gzp 27 15 net net JJ cord-209166-1drg5gzp 27 16 force force NN cord-209166-1drg5gzp 27 17 on on IN cord-209166-1drg5gzp 27 18 the the DT cord-209166-1drg5gzp 27 19 system system NN cord-209166-1drg5gzp 27 20 , , , cord-209166-1drg5gzp 27 21 and and CC cord-209166-1drg5gzp 27 22 a a DT cord-209166-1drg5gzp 27 23 liquid liquid JJ cord-209166-1drg5gzp 27 24 layer layer NN cord-209166-1drg5gzp 27 25 had have VBD cord-209166-1drg5gzp 27 26 completely completely RB cord-209166-1drg5gzp 27 27 engulfed engulf VBN cord-209166-1drg5gzp 27 28 the the DT cord-209166-1drg5gzp 27 29 metal metal NN cord-209166-1drg5gzp 27 30 ball ball NN cord-209166-1drg5gzp 27 31 . . . cord-209166-1drg5gzp 28 1 The the DT cord-209166-1drg5gzp 28 2 system system NN cord-209166-1drg5gzp 28 3 is be VBZ cord-209166-1drg5gzp 28 4 an an DT cord-209166-1drg5gzp 28 5 isolated isolated JJ cord-209166-1drg5gzp 28 6 one one CD cord-209166-1drg5gzp 28 7 , , , cord-209166-1drg5gzp 28 8 with with IN cord-209166-1drg5gzp 28 9 no no DT cord-209166-1drg5gzp 28 10 presence presence NN cord-209166-1drg5gzp 28 11 or or CC cord-209166-1drg5gzp 28 12 effect effect NN cord-209166-1drg5gzp 28 13 of of IN cord-209166-1drg5gzp 28 14 gravity gravity NN cord-209166-1drg5gzp 28 15 and and CC cord-209166-1drg5gzp 28 16 standard standard JJ cord-209166-1drg5gzp 28 17 atmospheric atmospheric JJ cord-209166-1drg5gzp 28 18 pressure pressure NN cord-209166-1drg5gzp 28 19 of of IN cord-209166-1drg5gzp 28 20 1 1 CD cord-209166-1drg5gzp 28 21 atm atm NN cord-209166-1drg5gzp 28 22 . . . cord-209166-1drg5gzp 29 1 The the DT cord-209166-1drg5gzp 29 2 physical physical JJ cord-209166-1drg5gzp 29 3 conditions condition NNS cord-209166-1drg5gzp 29 4 of of IN cord-209166-1drg5gzp 29 5 the the DT cord-209166-1drg5gzp 29 6 system system NN cord-209166-1drg5gzp 29 7 can can MD cord-209166-1drg5gzp 29 8 be be VB cord-209166-1drg5gzp 29 9 compared compare VBN cord-209166-1drg5gzp 29 10 to to IN cord-209166-1drg5gzp 29 11 that that DT cord-209166-1drg5gzp 29 12 present present JJ cord-209166-1drg5gzp 29 13 inside inside IN cord-209166-1drg5gzp 29 14 the the DT cord-209166-1drg5gzp 29 15 International international JJ cord-209166-1drg5gzp 29 16 space space NN cord-209166-1drg5gzp 29 17 station station NN cord-209166-1drg5gzp 29 18 where where WRB cord-209166-1drg5gzp 29 19 habitable habitable JJ cord-209166-1drg5gzp 29 20 conditions condition NNS cord-209166-1drg5gzp 29 21 are be VBP cord-209166-1drg5gzp 29 22 present present JJ cord-209166-1drg5gzp 29 23 with with IN cord-209166-1drg5gzp 29 24 the the DT cord-209166-1drg5gzp 29 25 exception exception NN cord-209166-1drg5gzp 29 26 of of IN cord-209166-1drg5gzp 29 27 gravity gravity NN cord-209166-1drg5gzp 29 28 .. .. . cord-209166-1drg5gzp 30 1 Now now RB cord-209166-1drg5gzp 30 2 the the DT cord-209166-1drg5gzp 30 3 complete complete JJ cord-209166-1drg5gzp 30 4 system system NN cord-209166-1drg5gzp 30 5 is be VBZ cord-209166-1drg5gzp 30 6 rotated rotate VBN cord-209166-1drg5gzp 30 7 with with IN cord-209166-1drg5gzp 30 8 a a DT cord-209166-1drg5gzp 30 9 constant constant JJ cord-209166-1drg5gzp 30 10 angular angular JJ cord-209166-1drg5gzp 30 11 velocity velocity NN cord-209166-1drg5gzp 30 12 ω ω NN cord-209166-1drg5gzp 30 13 and and CC cord-209166-1drg5gzp 30 14 was be VBD cord-209166-1drg5gzp 30 15 allowed allow VBN cord-209166-1drg5gzp 30 16 to to TO cord-209166-1drg5gzp 30 17 rotate rotate VB cord-209166-1drg5gzp 30 18 with with IN cord-209166-1drg5gzp 30 19 the the DT cord-209166-1drg5gzp 30 20 same same JJ cord-209166-1drg5gzp 30 21 angular angular JJ cord-209166-1drg5gzp 30 22 velocity velocity NN cord-209166-1drg5gzp 30 23 . . . cord-209166-1drg5gzp 31 1 We -PRON- PRP cord-209166-1drg5gzp 31 2 can can MD cord-209166-1drg5gzp 31 3 say say VB cord-209166-1drg5gzp 31 4 that that IN cord-209166-1drg5gzp 31 5 many many JJ cord-209166-1drg5gzp 31 6 forces force NNS cord-209166-1drg5gzp 31 7 are be VBP cord-209166-1drg5gzp 31 8 acting act VBG cord-209166-1drg5gzp 31 9 within within IN cord-209166-1drg5gzp 31 10 the the DT cord-209166-1drg5gzp 31 11 system system NN cord-209166-1drg5gzp 31 12 and and CC cord-209166-1drg5gzp 31 13 primary primary JJ cord-209166-1drg5gzp 31 14 one one NN cord-209166-1drg5gzp 31 15 will will MD cord-209166-1drg5gzp 31 16 be be VB cord-209166-1drg5gzp 31 17 the the DT cord-209166-1drg5gzp 31 18 gravitational gravitational JJ cord-209166-1drg5gzp 31 19 force force NN cord-209166-1drg5gzp 31 20 between between IN cord-209166-1drg5gzp 31 21 the the DT cord-209166-1drg5gzp 31 22 metal metal NN cord-209166-1drg5gzp 31 23 ball ball NN cord-209166-1drg5gzp 31 24 and and CC cord-209166-1drg5gzp 31 25 the the DT cord-209166-1drg5gzp 31 26 liquid liquid JJ cord-209166-1drg5gzp 31 27 layer layer NN cord-209166-1drg5gzp 31 28 . . . cord-209166-1drg5gzp 32 1 The the DT cord-209166-1drg5gzp 32 2 system system NN cord-209166-1drg5gzp 32 3 seems seem VBZ cord-209166-1drg5gzp 32 4 more more RBR cord-209166-1drg5gzp 32 5 or or CC cord-209166-1drg5gzp 32 6 like like IN cord-209166-1drg5gzp 32 7 a a DT cord-209166-1drg5gzp 32 8 planet planet NN cord-209166-1drg5gzp 32 9 with with IN cord-209166-1drg5gzp 32 10 a a DT cord-209166-1drg5gzp 32 11 solid solid JJ cord-209166-1drg5gzp 32 12 metallic metallic JJ cord-209166-1drg5gzp 32 13 core core NN cord-209166-1drg5gzp 32 14 and and CC cord-209166-1drg5gzp 32 15 a a DT cord-209166-1drg5gzp 32 16 liquid liquid JJ cord-209166-1drg5gzp 32 17 atmosphere atmosphere NN cord-209166-1drg5gzp 32 18 . . . cord-209166-1drg5gzp 33 1 But but CC cord-209166-1drg5gzp 33 2 we -PRON- PRP cord-209166-1drg5gzp 33 3 have have VBP cord-209166-1drg5gzp 33 4 taken take VBN cord-209166-1drg5gzp 33 5 effect effect NN cord-209166-1drg5gzp 33 6 to to IN cord-209166-1drg5gzp 33 7 to to TO cord-209166-1drg5gzp 33 8 gravitational gravitational VB cord-209166-1drg5gzp 33 9 forces force NNS cord-209166-1drg5gzp 33 10 to to TO cord-209166-1drg5gzp 33 11 be be VB cord-209166-1drg5gzp 33 12 very very RB cord-209166-1drg5gzp 33 13 negligible negligible JJ cord-209166-1drg5gzp 33 14 , , , cord-209166-1drg5gzp 33 15 since since IN cord-209166-1drg5gzp 33 16 the the DT cord-209166-1drg5gzp 33 17 mass mass NN cord-209166-1drg5gzp 33 18 of of IN cord-209166-1drg5gzp 33 19 the the DT cord-209166-1drg5gzp 33 20 metal metal NN cord-209166-1drg5gzp 33 21 ball ball NN cord-209166-1drg5gzp 33 22 as as RB cord-209166-1drg5gzp 33 23 well well RB cord-209166-1drg5gzp 33 24 as as IN cord-209166-1drg5gzp 33 25 that that DT cord-209166-1drg5gzp 33 26 of of IN cord-209166-1drg5gzp 33 27 the the DT cord-209166-1drg5gzp 33 28 liquid liquid JJ cord-209166-1drg5gzp 33 29 layer layer NN cord-209166-1drg5gzp 33 30 is be VBZ cord-209166-1drg5gzp 33 31 very very RB cord-209166-1drg5gzp 33 32 small small JJ cord-209166-1drg5gzp 33 33 . . . cord-209166-1drg5gzp 34 1 Also also RB cord-209166-1drg5gzp 34 2 the the DT cord-209166-1drg5gzp 34 3 Gravitational gravitational JJ cord-209166-1drg5gzp 34 4 constant constant JJ cord-209166-1drg5gzp 34 5 G g NN cord-209166-1drg5gzp 34 6 is be VBZ cord-209166-1drg5gzp 34 7 of of IN cord-209166-1drg5gzp 34 8 the the DT cord-209166-1drg5gzp 34 9 value value NN cord-209166-1drg5gzp 34 10 6.674 6.674 CD cord-209166-1drg5gzp 34 11 × × NN cord-209166-1drg5gzp 34 12 10 10 CD cord-209166-1drg5gzp 34 13 −11 −11 NNP cord-209166-1drg5gzp 34 14 m m NNP cord-209166-1drg5gzp 34 15 3 3 CD cord-209166-1drg5gzp 34 16 kg kg NN cord-209166-1drg5gzp 35 1 −1 −1 NNP cord-209166-1drg5gzp 35 2 s s POS cord-209166-1drg5gzp 35 3 −2 −2 NNP cord-209166-1drg5gzp 35 4 , , , cord-209166-1drg5gzp 35 5 which which WDT cord-209166-1drg5gzp 35 6 is be VBZ cord-209166-1drg5gzp 35 7 too too RB cord-209166-1drg5gzp 35 8 small small JJ cord-209166-1drg5gzp 35 9 to to TO cord-209166-1drg5gzp 35 10 make make VB cord-209166-1drg5gzp 35 11 the the DT cord-209166-1drg5gzp 35 12 gravitational gravitational JJ cord-209166-1drg5gzp 35 13 force force NN cord-209166-1drg5gzp 35 14 effective effective JJ cord-209166-1drg5gzp 35 15 for for IN cord-209166-1drg5gzp 35 16 calculations calculation NNS cord-209166-1drg5gzp 35 17 . . . cord-209166-1drg5gzp 36 1 Hence hence RB cord-209166-1drg5gzp 36 2 we -PRON- PRP cord-209166-1drg5gzp 36 3 have have VBP cord-209166-1drg5gzp 36 4 to to TO cord-209166-1drg5gzp 36 5 take take VB cord-209166-1drg5gzp 36 6 adhesion adhesion NN cord-209166-1drg5gzp 36 7 forces force NNS cord-209166-1drg5gzp 36 8 between between IN cord-209166-1drg5gzp 36 9 the the DT cord-209166-1drg5gzp 36 10 liquid liquid JJ cord-209166-1drg5gzp 36 11 particle particle NN cord-209166-1drg5gzp 36 12 and and CC cord-209166-1drg5gzp 36 13 metal metal NN cord-209166-1drg5gzp 36 14 , , , cord-209166-1drg5gzp 36 15 and and CC cord-209166-1drg5gzp 36 16 cohesion cohesion NN cord-209166-1drg5gzp 36 17 forces force NNS cord-209166-1drg5gzp 36 18 within within IN cord-209166-1drg5gzp 36 19 the the DT cord-209166-1drg5gzp 36 20 liquid liquid JJ cord-209166-1drg5gzp 36 21 particles particle NNS cord-209166-1drg5gzp 36 22 to to TO cord-209166-1drg5gzp 36 23 be be VB cord-209166-1drg5gzp 36 24 main main JJ cord-209166-1drg5gzp 36 25 cause cause NN cord-209166-1drg5gzp 36 26 for for IN cord-209166-1drg5gzp 36 27 keeping keep VBG cord-209166-1drg5gzp 36 28 the the DT cord-209166-1drg5gzp 36 29 complete complete JJ cord-209166-1drg5gzp 36 30 system system NN cord-209166-1drg5gzp 36 31 intact intact JJ cord-209166-1drg5gzp 36 32 . . . cord-209166-1drg5gzp 37 1 Let let VB cord-209166-1drg5gzp 37 2 the the DT cord-209166-1drg5gzp 37 3 radius radius NN cord-209166-1drg5gzp 37 4 of of IN cord-209166-1drg5gzp 37 5 the the DT cord-209166-1drg5gzp 37 6 metal metal NN cord-209166-1drg5gzp 37 7 ball ball NN cord-209166-1drg5gzp 37 8 be be VB cord-209166-1drg5gzp 37 9 R r NN cord-209166-1drg5gzp 37 10 and and CC cord-209166-1drg5gzp 37 11 the the DT cord-209166-1drg5gzp 37 12 initial initial JJ cord-209166-1drg5gzp 37 13 height height NN cord-209166-1drg5gzp 37 14 of of IN cord-209166-1drg5gzp 37 15 the the DT cord-209166-1drg5gzp 37 16 liquid liquid JJ cord-209166-1drg5gzp 37 17 layer layer NN cord-209166-1drg5gzp 37 18 is be VBZ cord-209166-1drg5gzp 37 19 taken take VBN cord-209166-1drg5gzp 37 20 to to TO cord-209166-1drg5gzp 37 21 be be VB cord-209166-1drg5gzp 37 22 m. m. NN cord-209166-1drg5gzp 38 1 Now now RB cord-209166-1drg5gzp 38 2 the the DT cord-209166-1drg5gzp 38 3 system system NN cord-209166-1drg5gzp 38 4 is be VBZ cord-209166-1drg5gzp 38 5 made make VBN cord-209166-1drg5gzp 38 6 up up RP cord-209166-1drg5gzp 38 7 of of IN cord-209166-1drg5gzp 38 8 material material NN cord-209166-1drg5gzp 38 9 of of IN cord-209166-1drg5gzp 38 10 different different JJ cord-209166-1drg5gzp 38 11 densities density NNS cord-209166-1drg5gzp 38 12 . . . cord-209166-1drg5gzp 39 1 Let let VB cord-209166-1drg5gzp 39 2 the the DT cord-209166-1drg5gzp 39 3 density density NN cord-209166-1drg5gzp 39 4 of of IN cord-209166-1drg5gzp 39 5 the the DT cord-209166-1drg5gzp 39 6 liquid liquid JJ cord-209166-1drg5gzp 39 7 layer layer NN cord-209166-1drg5gzp 39 8 surrounding surround VBG cord-209166-1drg5gzp 39 9 it -PRON- PRP cord-209166-1drg5gzp 39 10 be be VB cord-209166-1drg5gzp 39 11 ρ ρ NFP cord-209166-1drg5gzp 39 12 and and CC cord-209166-1drg5gzp 39 13 that that DT cord-209166-1drg5gzp 39 14 of of IN cord-209166-1drg5gzp 39 15 the the DT cord-209166-1drg5gzp 39 16 metal metal NN cord-209166-1drg5gzp 39 17 ball ball NN cord-209166-1drg5gzp 39 18 be be VB cord-209166-1drg5gzp 39 19 ρ ρ NNP cord-209166-1drg5gzp 39 20 m m NNP cord-209166-1drg5gzp 39 21 respectively respectively RB cord-209166-1drg5gzp 39 22 . . . cord-209166-1drg5gzp 40 1 Now now RB cord-209166-1drg5gzp 40 2 from from IN cord-209166-1drg5gzp 40 3 the the DT cord-209166-1drg5gzp 40 4 initial initial JJ cord-209166-1drg5gzp 40 5 state state NN cord-209166-1drg5gzp 40 6 , , , cord-209166-1drg5gzp 40 7 since since IN cord-209166-1drg5gzp 40 8 the the DT cord-209166-1drg5gzp 40 9 complete complete JJ cord-209166-1drg5gzp 40 10 system system NN cord-209166-1drg5gzp 40 11 is be VBZ cord-209166-1drg5gzp 40 12 being be VBG cord-209166-1drg5gzp 40 13 rotated rotate VBN cord-209166-1drg5gzp 40 14 , , , cord-209166-1drg5gzp 40 15 then then RB cord-209166-1drg5gzp 40 16 the the DT cord-209166-1drg5gzp 40 17 shape shape NN cord-209166-1drg5gzp 40 18 of of IN cord-209166-1drg5gzp 40 19 the the DT cord-209166-1drg5gzp 40 20 metal metal NN cord-209166-1drg5gzp 40 21 ball ball NN cord-209166-1drg5gzp 40 22 wo will MD cord-209166-1drg5gzp 40 23 n't not RB cord-209166-1drg5gzp 40 24 change change VB cord-209166-1drg5gzp 40 25 , , , cord-209166-1drg5gzp 40 26 but but CC cord-209166-1drg5gzp 40 27 the the DT cord-209166-1drg5gzp 40 28 shape shape NN cord-209166-1drg5gzp 40 29 of of IN cord-209166-1drg5gzp 40 30 the the DT cord-209166-1drg5gzp 40 31 liquid liquid JJ cord-209166-1drg5gzp 40 32 layer layer NN cord-209166-1drg5gzp 40 33 will will MD cord-209166-1drg5gzp 40 34 change change VB cord-209166-1drg5gzp 40 35 due due IN cord-209166-1drg5gzp 40 36 to to IN cord-209166-1drg5gzp 40 37 non non JJ cord-209166-1drg5gzp 40 38 - - JJ cord-209166-1drg5gzp 40 39 rigid rigid JJ cord-209166-1drg5gzp 40 40 properties property NNS cord-209166-1drg5gzp 40 41 of of IN cord-209166-1drg5gzp 40 42 it -PRON- PRP cord-209166-1drg5gzp 40 43 . . . cord-209166-1drg5gzp 41 1 Due due IN cord-209166-1drg5gzp 41 2 to to IN cord-209166-1drg5gzp 41 3 presence presence NN cord-209166-1drg5gzp 41 4 of of IN cord-209166-1drg5gzp 41 5 centrifugal centrifugal JJ cord-209166-1drg5gzp 41 6 force force NN cord-209166-1drg5gzp 41 7 , , , cord-209166-1drg5gzp 41 8 the the DT cord-209166-1drg5gzp 41 9 liquid liquid NN cord-209166-1drg5gzp 41 10 will will MD cord-209166-1drg5gzp 41 11 try try VB cord-209166-1drg5gzp 41 12 to to TO cord-209166-1drg5gzp 41 13 flatten flatten VB cord-209166-1drg5gzp 41 14 out out RP cord-209166-1drg5gzp 41 15 in in IN cord-209166-1drg5gzp 41 16 the the DT cord-209166-1drg5gzp 41 17 space space NN cord-209166-1drg5gzp 41 18 along along IN cord-209166-1drg5gzp 41 19 equatorial equatorial JJ cord-209166-1drg5gzp 41 20 plane plane NN cord-209166-1drg5gzp 41 21 , , , cord-209166-1drg5gzp 41 22 resulting result VBG cord-209166-1drg5gzp 41 23 in in IN cord-209166-1drg5gzp 41 24 the the DT cord-209166-1drg5gzp 41 25 formation formation NN cord-209166-1drg5gzp 41 26 of of IN cord-209166-1drg5gzp 41 27 a a DT cord-209166-1drg5gzp 41 28 spheroid spheroid NN cord-209166-1drg5gzp 41 29 shaped shape VBN cord-209166-1drg5gzp 41 30 drop drop NN cord-209166-1drg5gzp 41 31 of of IN cord-209166-1drg5gzp 41 32 liquid liquid NN cord-209166-1drg5gzp 41 33 surrounding surround VBG cord-209166-1drg5gzp 41 34 the the DT cord-209166-1drg5gzp 41 35 spherical spherical JJ cord-209166-1drg5gzp 41 36 metal metal NN cord-209166-1drg5gzp 41 37 ball ball NN cord-209166-1drg5gzp 41 38 . . . cord-209166-1drg5gzp 42 1 According accord VBG cord-209166-1drg5gzp 42 2 to to IN cord-209166-1drg5gzp 42 3 the the DT cord-209166-1drg5gzp 42 4 section section NN cord-209166-1drg5gzp 42 5 2 2 CD cord-209166-1drg5gzp 42 6 , , , cord-209166-1drg5gzp 42 7 as as IN cord-209166-1drg5gzp 42 8 the the DT cord-209166-1drg5gzp 42 9 value value NN cord-209166-1drg5gzp 42 10 of of IN cord-209166-1drg5gzp 42 11 angular angular JJ cord-209166-1drg5gzp 42 12 velocity velocity NN cord-209166-1drg5gzp 42 13 increases increase VBZ cord-209166-1drg5gzp 42 14 the the DT cord-209166-1drg5gzp 42 15 height height NN cord-209166-1drg5gzp 42 16 of of IN cord-209166-1drg5gzp 42 17 fluid fluid JJ cord-209166-1drg5gzp 42 18 layer layer NN cord-209166-1drg5gzp 42 19 ( ( -LRB- cord-209166-1drg5gzp 42 20 m m NNP cord-209166-1drg5gzp 42 21 ) ) -RRB- cord-209166-1drg5gzp 42 22 along along IN cord-209166-1drg5gzp 42 23 Z− Z− NNP cord-209166-1drg5gzp 42 24 axis axis NN cord-209166-1drg5gzp 42 25 will will MD cord-209166-1drg5gzp 42 26 decrease decrease VB cord-209166-1drg5gzp 42 27 resulting result VBG cord-209166-1drg5gzp 42 28 an an DT cord-209166-1drg5gzp 42 29 equatorial equatorial JJ cord-209166-1drg5gzp 42 30 bulge bulge NN cord-209166-1drg5gzp 42 31 along along IN cord-209166-1drg5gzp 42 32 XY XY NNP cord-209166-1drg5gzp 42 33 plane plane NN cord-209166-1drg5gzp 42 34 . . . cord-209166-1drg5gzp 43 1 Let let VB cord-209166-1drg5gzp 43 2 the the DT cord-209166-1drg5gzp 43 3 decrease decrease NN cord-209166-1drg5gzp 43 4 of of IN cord-209166-1drg5gzp 43 5 fluid fluid JJ cord-209166-1drg5gzp 43 6 layer layer NN cord-209166-1drg5gzp 43 7 along along IN cord-209166-1drg5gzp 43 8 Z−axis z−axi NNS cord-209166-1drg5gzp 43 9 be be VB cord-209166-1drg5gzp 43 10 h h NNP cord-209166-1drg5gzp 43 11 and and CC cord-209166-1drg5gzp 43 12 Let let VB cord-209166-1drg5gzp 43 13 the the DT cord-209166-1drg5gzp 43 14 value value NN cord-209166-1drg5gzp 43 15 of of IN cord-209166-1drg5gzp 43 16 the the DT cord-209166-1drg5gzp 43 17 bulge bulge NN cord-209166-1drg5gzp 43 18 be be VB cord-209166-1drg5gzp 43 19 n. n. NN cord-209166-1drg5gzp 44 1 Since since IN cord-209166-1drg5gzp 44 2 the the DT cord-209166-1drg5gzp 44 3 volume volume NN cord-209166-1drg5gzp 44 4 of of IN cord-209166-1drg5gzp 44 5 the the DT cord-209166-1drg5gzp 44 6 fluid fluid NN cord-209166-1drg5gzp 44 7 is be VBZ cord-209166-1drg5gzp 44 8 constant constant JJ cord-209166-1drg5gzp 44 9 throughout throughout IN cord-209166-1drg5gzp 44 10 the the DT cord-209166-1drg5gzp 44 11 process process NN cord-209166-1drg5gzp 44 12 , , , cord-209166-1drg5gzp 44 13 to to TO cord-209166-1drg5gzp 44 14 calculate calculate VB cord-209166-1drg5gzp 44 15 the the DT cord-209166-1drg5gzp 44 16 value value NN cord-209166-1drg5gzp 44 17 of of IN cord-209166-1drg5gzp 44 18 the the DT cord-209166-1drg5gzp 44 19 bulge bulge NN cord-209166-1drg5gzp 44 20 we -PRON- PRP cord-209166-1drg5gzp 44 21 are be VBP cord-209166-1drg5gzp 44 22 going go VBG cord-209166-1drg5gzp 44 23 to to TO cord-209166-1drg5gzp 44 24 conserve conserve VB cord-209166-1drg5gzp 44 25 the the DT cord-209166-1drg5gzp 44 26 volume volume NN cord-209166-1drg5gzp 44 27 of of IN cord-209166-1drg5gzp 44 28 initial initial JJ cord-209166-1drg5gzp 44 29 state state NN cord-209166-1drg5gzp 44 30 and and CC cord-209166-1drg5gzp 44 31 final final JJ cord-209166-1drg5gzp 44 32 state state NN cord-209166-1drg5gzp 44 33 . . . cord-209166-1drg5gzp 45 1 Let let VB cord-209166-1drg5gzp 45 2 the the DT cord-209166-1drg5gzp 45 3 volume volume NN cord-209166-1drg5gzp 45 4 of of IN cord-209166-1drg5gzp 45 5 liquid liquid NN cord-209166-1drg5gzp 45 6 at at IN cord-209166-1drg5gzp 45 7 initial initial JJ cord-209166-1drg5gzp 45 8 state state NN cord-209166-1drg5gzp 45 9 be be VB cord-209166-1drg5gzp 45 10 V v NN cord-209166-1drg5gzp 45 11 1 1 CD cord-209166-1drg5gzp 45 12 and and CC cord-209166-1drg5gzp 45 13 that that IN cord-209166-1drg5gzp 45 14 at at IN cord-209166-1drg5gzp 45 15 final final JJ cord-209166-1drg5gzp 45 16 state state NN cord-209166-1drg5gzp 45 17 be be VB cord-209166-1drg5gzp 45 18 V V NNP cord-209166-1drg5gzp 45 19 2 2 CD cord-209166-1drg5gzp 45 20 , , , cord-209166-1drg5gzp 45 21 so so CC cord-209166-1drg5gzp 45 22 we -PRON- PRP cord-209166-1drg5gzp 45 23 have have VBP cord-209166-1drg5gzp 45 24 : : : cord-209166-1drg5gzp 46 1 Since since IN cord-209166-1drg5gzp 46 2 V v NN cord-209166-1drg5gzp 46 3 1 1 CD cord-209166-1drg5gzp 46 4 = = SYM cord-209166-1drg5gzp 46 5 V v NN cord-209166-1drg5gzp 46 6 2 2 CD cord-209166-1drg5gzp 46 7 , , , cord-209166-1drg5gzp 46 8 we -PRON- PRP cord-209166-1drg5gzp 46 9 can can MD cord-209166-1drg5gzp 46 10 write write VB cord-209166-1drg5gzp 46 11 : : : cord-209166-1drg5gzp 46 12 _SP cord-209166-1drg5gzp 47 1 So so CC cord-209166-1drg5gzp 47 2 Finally finally RB cord-209166-1drg5gzp 47 3 we -PRON- PRP cord-209166-1drg5gzp 47 4 have have VBP cord-209166-1drg5gzp 47 5 the the DT cord-209166-1drg5gzp 47 6 lengths length NNS cord-209166-1drg5gzp 47 7 of of IN cord-209166-1drg5gzp 47 8 all all DT cord-209166-1drg5gzp 47 9 semi semi JJ cord-209166-1drg5gzp 47 10 major major JJ cord-209166-1drg5gzp 47 11 axes axis NNS cord-209166-1drg5gzp 47 12 of of IN cord-209166-1drg5gzp 47 13 the the DT cord-209166-1drg5gzp 47 14 spheroid spheroid NN cord-209166-1drg5gzp 48 1 So so CC cord-209166-1drg5gzp 48 2 Equation equation NN cord-209166-1drg5gzp 48 3 of of IN cord-209166-1drg5gzp 48 4 the the DT cord-209166-1drg5gzp 48 5 spheroid spheroid NN cord-209166-1drg5gzp 48 6 will will MD cord-209166-1drg5gzp 48 7 be be VB cord-209166-1drg5gzp 48 8 : : : cord-209166-1drg5gzp 49 1 3 3 LS cord-209166-1drg5gzp 49 2 Pressure Pressure NNP cord-209166-1drg5gzp 49 3 Potential Potential NNP cord-209166-1drg5gzp 49 4 and and CC cord-209166-1drg5gzp 49 5 containing contain VBG cord-209166-1drg5gzp 49 6 force force NN cord-209166-1drg5gzp 49 7 Consider consider VB cord-209166-1drg5gzp 49 8 the the DT cord-209166-1drg5gzp 49 9 equilibrium equilibrium NN cord-209166-1drg5gzp 49 10 of of IN cord-209166-1drg5gzp 49 11 an an DT cord-209166-1drg5gzp 49 12 incompressible incompressible JJ cord-209166-1drg5gzp 49 13 fluid fluid NN cord-209166-1drg5gzp 49 14 with with IN cord-209166-1drg5gzp 49 15 a a DT cord-209166-1drg5gzp 49 16 constant constant JJ cord-209166-1drg5gzp 49 17 angular angular JJ cord-209166-1drg5gzp 49 18 velocity velocity NN cord-209166-1drg5gzp 49 19 ω ω NN cord-209166-1drg5gzp 49 20 in in IN cord-209166-1drg5gzp 49 21 some some DT cord-209166-1drg5gzp 49 22 inertial inertial JJ cord-209166-1drg5gzp 49 23 frame frame NN cord-209166-1drg5gzp 49 24 of of IN cord-209166-1drg5gzp 49 25 reference reference NN cord-209166-1drg5gzp 49 26 . . . cord-209166-1drg5gzp 50 1 According accord VBG cord-209166-1drg5gzp 50 2 to to IN cord-209166-1drg5gzp 50 3 standard standard JJ cord-209166-1drg5gzp 50 4 Newtonian Newtonian NNP cord-209166-1drg5gzp 50 5 Dynamics Dynamics NNPS cord-209166-1drg5gzp 50 6 the the DT cord-209166-1drg5gzp 50 7 force force NN cord-209166-1drg5gzp 50 8 balance balance NN cord-209166-1drg5gzp 50 9 equation equation NN cord-209166-1drg5gzp 50 10 takes take VBZ cord-209166-1drg5gzp 50 11 form form NN cord-209166-1drg5gzp 51 1 Where where WRB cord-209166-1drg5gzp 51 2 ∇p ∇p EX cord-209166-1drg5gzp 51 3 is be VBZ cord-209166-1drg5gzp 51 4 the the DT cord-209166-1drg5gzp 51 5 static static JJ cord-209166-1drg5gzp 51 6 fluid fluid JJ cord-209166-1drg5gzp 51 7 pressure pressure NN cord-209166-1drg5gzp 51 8 , , , cord-209166-1drg5gzp 51 9 ρ ρ NNP cord-209166-1drg5gzp 51 10 is be VBZ cord-209166-1drg5gzp 51 11 the the DT cord-209166-1drg5gzp 51 12 mass mass NN cord-209166-1drg5gzp 51 13 density density NN cord-209166-1drg5gzp 51 14 and and CC cord-209166-1drg5gzp 51 15 in in IN cord-209166-1drg5gzp 51 16 our -PRON- PRP$ cord-209166-1drg5gzp 51 17 case case NN cord-209166-1drg5gzp 51 18 Ψ ψ NN cord-209166-1drg5gzp 51 19 is be VBZ cord-209166-1drg5gzp 51 20 the the DT cord-209166-1drg5gzp 51 21 potential potential NN cord-209166-1drg5gzp 51 22 for for IN cord-209166-1drg5gzp 51 23 containing contain VBG cord-209166-1drg5gzp 51 24 force force NN cord-209166-1drg5gzp 51 25 . . . cord-209166-1drg5gzp 52 1 So so RB cord-209166-1drg5gzp 52 2 the the DT cord-209166-1drg5gzp 52 3 Equation equation NN cord-209166-1drg5gzp 52 4 can can MD cord-209166-1drg5gzp 52 5 be be VB cord-209166-1drg5gzp 52 6 modified modify VBN cord-209166-1drg5gzp 52 7 into into IN cord-209166-1drg5gzp 52 8 Where where WRB cord-209166-1drg5gzp 52 9 Ψ Ψ NNP cord-209166-1drg5gzp 52 10 is be VBZ cord-209166-1drg5gzp 52 11 the the DT cord-209166-1drg5gzp 52 12 centrifugal centrifugal JJ cord-209166-1drg5gzp 52 13 potential potential NN cord-209166-1drg5gzp 52 14 , , , cord-209166-1drg5gzp 52 15 Ψ ψ NN cord-209166-1drg5gzp 52 16 = = SYM cord-209166-1drg5gzp 52 17 − − NN cord-209166-1drg5gzp 52 18 ω(x ω(x CD cord-209166-1drg5gzp 52 19 2 2 CD cord-209166-1drg5gzp 52 20 + + CC cord-209166-1drg5gzp 52 21 y y NN cord-209166-1drg5gzp 52 22 2 2 CD cord-209166-1drg5gzp 52 23 ) ) -RRB- cord-209166-1drg5gzp 52 24 2 2 CD cord-209166-1drg5gzp 53 1 So so RB cord-209166-1drg5gzp 53 2 , , , cord-209166-1drg5gzp 53 3 the the DT cord-209166-1drg5gzp 53 4 equation equation NN cord-209166-1drg5gzp 53 5 becomes become VBZ cord-209166-1drg5gzp 53 6 Where where WRB cord-209166-1drg5gzp 53 7 P p NN cord-209166-1drg5gzp 53 8 0 0 CD cord-209166-1drg5gzp 53 9 is be VBZ cord-209166-1drg5gzp 53 10 Central Central NNP cord-209166-1drg5gzp 53 11 Fluid Fluid NNP cord-209166-1drg5gzp 53 12 Pressure Pressure NNP cord-209166-1drg5gzp 53 13 and and CC cord-209166-1drg5gzp 53 14 the the DT cord-209166-1drg5gzp 53 15 pressure pressure NN cord-209166-1drg5gzp 53 16 at at IN cord-209166-1drg5gzp 53 17 the the DT cord-209166-1drg5gzp 53 18 outer outer JJ cord-209166-1drg5gzp 53 19 boundary boundary NN cord-209166-1drg5gzp 53 20 of of IN cord-209166-1drg5gzp 53 21 the the DT cord-209166-1drg5gzp 53 22 fluid fluid JJ cord-209166-1drg5gzp 53 23 surface surface NN cord-209166-1drg5gzp 53 24 must must MD cord-209166-1drg5gzp 53 25 be be VB cord-209166-1drg5gzp 53 26 zero zero CD cord-209166-1drg5gzp 53 27 , , , cord-209166-1drg5gzp 53 28 otherwise otherwise RB cord-209166-1drg5gzp 53 29 there there EX cord-209166-1drg5gzp 53 30 would would MD cord-209166-1drg5gzp 53 31 be be VB cord-209166-1drg5gzp 53 32 a a DT cord-209166-1drg5gzp 53 33 force force NN cord-209166-1drg5gzp 53 34 imbalance imbalance NN cord-209166-1drg5gzp 53 35 across across IN cord-209166-1drg5gzp 53 36 the the DT cord-209166-1drg5gzp 53 37 boundary boundary NN cord-209166-1drg5gzp 53 38 . . . cord-209166-1drg5gzp 54 1 Hence hence RB cord-209166-1drg5gzp 54 2 P p NN cord-209166-1drg5gzp 54 3 = = SYM cord-209166-1drg5gzp 54 4 0 0 NFP cord-209166-1drg5gzp 54 5 which which WDT cord-209166-1drg5gzp 54 6 implies imply VBZ cord-209166-1drg5gzp 54 7 Now now RB cord-209166-1drg5gzp 54 8 as as IN cord-209166-1drg5gzp 54 9 we -PRON- PRP cord-209166-1drg5gzp 54 10 know know VBP cord-209166-1drg5gzp 54 11 , , , cord-209166-1drg5gzp 54 12 the the DT cord-209166-1drg5gzp 54 13 effect effect NN cord-209166-1drg5gzp 54 14 of of IN cord-209166-1drg5gzp 54 15 gravitational gravitational JJ cord-209166-1drg5gzp 54 16 potential potential NN cord-209166-1drg5gzp 54 17 is be VBZ cord-209166-1drg5gzp 54 18 much much RB cord-209166-1drg5gzp 54 19 minimal minimal JJ cord-209166-1drg5gzp 54 20 than than IN cord-209166-1drg5gzp 54 21 another another DT cord-209166-1drg5gzp 54 22 potential potential JJ cord-209166-1drg5gzp 54 23 taken take VBN cord-209166-1drg5gzp 54 24 under under IN cord-209166-1drg5gzp 54 25 consideration consideration NN cord-209166-1drg5gzp 54 26 in in IN cord-209166-1drg5gzp 54 27 the the DT cord-209166-1drg5gzp 54 28 equation equation NN cord-209166-1drg5gzp 54 29 for for IN cord-209166-1drg5gzp 54 30 Central central JJ cord-209166-1drg5gzp 54 31 fluid fluid JJ cord-209166-1drg5gzp 54 32 pressure pressure NN cord-209166-1drg5gzp 54 33 . . . cord-209166-1drg5gzp 55 1 The the DT cord-209166-1drg5gzp 55 2 cause cause NN cord-209166-1drg5gzp 55 3 of of IN cord-209166-1drg5gzp 55 4 this this DT cord-209166-1drg5gzp 55 5 potential potential NN cord-209166-1drg5gzp 55 6 can can MD cord-209166-1drg5gzp 55 7 be be VB cord-209166-1drg5gzp 55 8 explained explain VBN cord-209166-1drg5gzp 55 9 by by IN cord-209166-1drg5gzp 55 10 presence presence NN cord-209166-1drg5gzp 55 11 of of IN cord-209166-1drg5gzp 55 12 another another DT cord-209166-1drg5gzp 55 13 form form NN cord-209166-1drg5gzp 55 14 of of IN cord-209166-1drg5gzp 55 15 force force NN cord-209166-1drg5gzp 55 16 different different JJ cord-209166-1drg5gzp 55 17 from from IN cord-209166-1drg5gzp 55 18 the the DT cord-209166-1drg5gzp 55 19 gravitational gravitational JJ cord-209166-1drg5gzp 55 20 one one CD cord-209166-1drg5gzp 55 21 . . . cord-209166-1drg5gzp 56 1 This this DT cord-209166-1drg5gzp 56 2 force force NN cord-209166-1drg5gzp 56 3 in in IN cord-209166-1drg5gzp 56 4 some some DT cord-209166-1drg5gzp 56 5 form form NN cord-209166-1drg5gzp 56 6 , , , cord-209166-1drg5gzp 56 7 is be VBZ cord-209166-1drg5gzp 56 8 related relate VBN cord-209166-1drg5gzp 56 9 to to IN cord-209166-1drg5gzp 56 10 the the DT cord-209166-1drg5gzp 56 11 surface surface NN cord-209166-1drg5gzp 56 12 formation formation NN cord-209166-1drg5gzp 56 13 of of IN cord-209166-1drg5gzp 56 14 the the DT cord-209166-1drg5gzp 56 15 liquid liquid NN cord-209166-1drg5gzp 56 16 , , , cord-209166-1drg5gzp 56 17 which which WDT cord-209166-1drg5gzp 56 18 also also RB cord-209166-1drg5gzp 56 19 includes include VBZ cord-209166-1drg5gzp 56 20 surface surface NN cord-209166-1drg5gzp 56 21 tension tension NN cord-209166-1drg5gzp 56 22 ( ( -LRB- cord-209166-1drg5gzp 56 23 γ γ NN cord-209166-1drg5gzp 56 24 ) ) -RRB- cord-209166-1drg5gzp 56 25 of of IN cord-209166-1drg5gzp 56 26 the the DT cord-209166-1drg5gzp 56 27 fluid fluid NN cord-209166-1drg5gzp 56 28 in in IN cord-209166-1drg5gzp 56 29 the the DT cord-209166-1drg5gzp 56 30 potential potential JJ cord-209166-1drg5gzp 56 31 equation equation NN cord-209166-1drg5gzp 56 32 . . . cord-209166-1drg5gzp 57 1 Now now RB cord-209166-1drg5gzp 57 2 surface surface VB cord-209166-1drg5gzp 57 3 tension tension NN cord-209166-1drg5gzp 57 4 of of IN cord-209166-1drg5gzp 57 5 the the DT cord-209166-1drg5gzp 57 6 fluid fluid JJ cord-209166-1drg5gzp 57 7 leads lead VBZ cord-209166-1drg5gzp 57 8 to to IN cord-209166-1drg5gzp 57 9 The the DT cord-209166-1drg5gzp 57 10 Laplace Laplace NNP cord-209166-1drg5gzp 57 11 pressure pressure NN cord-209166-1drg5gzp 57 12 , , , cord-209166-1drg5gzp 57 13 which which WDT cord-209166-1drg5gzp 57 14 is be VBZ cord-209166-1drg5gzp 57 15 the the DT cord-209166-1drg5gzp 57 16 pressure pressure NN cord-209166-1drg5gzp 57 17 difference difference NN cord-209166-1drg5gzp 57 18 between between IN cord-209166-1drg5gzp 57 19 the the DT cord-209166-1drg5gzp 57 20 inside inside NN cord-209166-1drg5gzp 57 21 and and CC cord-209166-1drg5gzp 57 22 the the DT cord-209166-1drg5gzp 57 23 outside outside NN cord-209166-1drg5gzp 57 24 of of IN cord-209166-1drg5gzp 57 25 a a DT cord-209166-1drg5gzp 57 26 curved curved JJ cord-209166-1drg5gzp 57 27 surface surface NN cord-209166-1drg5gzp 57 28 that that WDT cord-209166-1drg5gzp 57 29 forms form VBZ cord-209166-1drg5gzp 57 30 the the DT cord-209166-1drg5gzp 57 31 boundary boundary NN cord-209166-1drg5gzp 57 32 between between IN cord-209166-1drg5gzp 57 33 a a DT cord-209166-1drg5gzp 57 34 gas gas NN cord-209166-1drg5gzp 57 35 region region NN cord-209166-1drg5gzp 57 36 and and CC cord-209166-1drg5gzp 57 37 a a DT cord-209166-1drg5gzp 57 38 liquid liquid JJ cord-209166-1drg5gzp 57 39 region region NN cord-209166-1drg5gzp 57 40 , , , cord-209166-1drg5gzp 57 41 and and CC cord-209166-1drg5gzp 57 42 is be VBZ cord-209166-1drg5gzp 57 43 given give VBN cord-209166-1drg5gzp 57 44 by by IN cord-209166-1drg5gzp 57 45 : : : cord-209166-1drg5gzp 57 46 Where where WRB cord-209166-1drg5gzp 57 47 R r NN cord-209166-1drg5gzp 57 48 1 1 CD cord-209166-1drg5gzp 57 49 and and CC cord-209166-1drg5gzp 57 50 R R NNP cord-209166-1drg5gzp 57 51 2 2 CD cord-209166-1drg5gzp 57 52 are be VBP cord-209166-1drg5gzp 57 53 the the DT cord-209166-1drg5gzp 57 54 principle principle JJ cord-209166-1drg5gzp 57 55 radii radii VBP cord-209166-1drg5gzp 57 56 curvature curvature NN cord-209166-1drg5gzp 57 57 of of IN cord-209166-1drg5gzp 57 58 the the DT cord-209166-1drg5gzp 57 59 fluid fluid JJ cord-209166-1drg5gzp 57 60 layer layer NN cord-209166-1drg5gzp 57 61 . . . cord-209166-1drg5gzp 58 1 And and CC cord-209166-1drg5gzp 58 2 hence hence RB cord-209166-1drg5gzp 58 3 , , , cord-209166-1drg5gzp 58 4 pressure pressure NN cord-209166-1drg5gzp 58 5 due due IN cord-209166-1drg5gzp 58 6 to to IN cord-209166-1drg5gzp 58 7 the the DT cord-209166-1drg5gzp 58 8 potential potential NN cord-209166-1drg5gzp 58 9 for for IN cord-209166-1drg5gzp 58 10 containing contain VBG cord-209166-1drg5gzp 58 11 force force NN cord-209166-1drg5gzp 58 12 can can MD cord-209166-1drg5gzp 58 13 be be VB cord-209166-1drg5gzp 58 14 represented represent VBN cord-209166-1drg5gzp 58 15 by by IN cord-209166-1drg5gzp 58 16 : : : cord-209166-1drg5gzp 58 17 So so RB cord-209166-1drg5gzp 58 18 the the DT cord-209166-1drg5gzp 58 19 final final JJ cord-209166-1drg5gzp 58 20 Equation equation NN cord-209166-1drg5gzp 58 21 for for IN cord-209166-1drg5gzp 58 22 containing contain VBG cord-209166-1drg5gzp 58 23 force force NN cord-209166-1drg5gzp 58 24 potential potential NN cord-209166-1drg5gzp 58 25 is be VBZ cord-209166-1drg5gzp 58 26 : : : cord-209166-1drg5gzp 58 27 For for IN cord-209166-1drg5gzp 58 28 General General NNP cord-209166-1drg5gzp 58 29 Ellipsoid Ellipsoid NNP cord-209166-1drg5gzp 58 30 , , , cord-209166-1drg5gzp 58 31 the the DT cord-209166-1drg5gzp 58 32 principle principle JJ cord-209166-1drg5gzp 58 33 radii radii VBP cord-209166-1drg5gzp 58 34 of of IN cord-209166-1drg5gzp 58 35 curvature curvature NN cord-209166-1drg5gzp 58 36 depend depend VB cord-209166-1drg5gzp 58 37 on on IN cord-209166-1drg5gzp 58 38 the the DT cord-209166-1drg5gzp 58 39 Mean Mean NNP cord-209166-1drg5gzp 58 40 Curvature(H Curvature(H NNP cord-209166-1drg5gzp 58 41 ) ) -RRB- cord-209166-1drg5gzp 58 42 and and CC cord-209166-1drg5gzp 58 43 the the DT cord-209166-1drg5gzp 58 44 Gaussian gaussian JJ cord-209166-1drg5gzp 58 45 Curvature(K curvature(k NN cord-209166-1drg5gzp 58 46 ) ) -RRB- cord-209166-1drg5gzp 58 47 [ [ -LRB- cord-209166-1drg5gzp 58 48 1 1 CD cord-209166-1drg5gzp 58 49 ] ] -RRB- cord-209166-1drg5gzp 58 50 . . . cord-209166-1drg5gzp 59 1 Hence hence RB cord-209166-1drg5gzp 59 2 , , , cord-209166-1drg5gzp 59 3 That that DT cord-209166-1drg5gzp 59 4 means mean VBZ cord-209166-1drg5gzp 59 5 equation equation NN cord-209166-1drg5gzp 59 6 7 7 CD cord-209166-1drg5gzp 59 7 can can MD cord-209166-1drg5gzp 59 8 be be VB cord-209166-1drg5gzp 59 9 modified modify VBN cord-209166-1drg5gzp 59 10 as as IN cord-209166-1drg5gzp 59 11 : : : cord-209166-1drg5gzp 59 12 Now now RB cord-209166-1drg5gzp 59 13 , , , cord-209166-1drg5gzp 59 14 As as IN cord-209166-1drg5gzp 59 15 we -PRON- PRP cord-209166-1drg5gzp 59 16 know know VBP cord-209166-1drg5gzp 59 17 that that IN cord-209166-1drg5gzp 59 18 H h NN cord-209166-1drg5gzp 59 19 = = . cord-209166-1drg5gzp 59 20 So so RB cord-209166-1drg5gzp 59 21 we -PRON- PRP cord-209166-1drg5gzp 59 22 get get VBP cord-209166-1drg5gzp 59 23 the the DT cord-209166-1drg5gzp 59 24 general general JJ cord-209166-1drg5gzp 59 25 form form NN cord-209166-1drg5gzp 59 26 of of IN cord-209166-1drg5gzp 59 27 potential potential NN cord-209166-1drg5gzp 59 28 ; ; : cord-209166-1drg5gzp 59 29 So so RB cord-209166-1drg5gzp 59 30 , , , cord-209166-1drg5gzp 59 31 the the DT cord-209166-1drg5gzp 59 32 General general JJ cord-209166-1drg5gzp 59 33 form form NN cord-209166-1drg5gzp 59 34 of of IN cord-209166-1drg5gzp 59 35 Containing contain VBG cord-209166-1drg5gzp 59 36 force force NN cord-209166-1drg5gzp 59 37 will will MD cord-209166-1drg5gzp 59 38 be be VB cord-209166-1drg5gzp 59 39 Hence hence RB cord-209166-1drg5gzp 59 40 ; ; : cord-209166-1drg5gzp 59 41 Now now RB cord-209166-1drg5gzp 59 42 to to TO cord-209166-1drg5gzp 59 43 analyse analyse VB cord-209166-1drg5gzp 59 44 the the DT cord-209166-1drg5gzp 59 45 potential potential NN cord-209166-1drg5gzp 59 46 and and CC cord-209166-1drg5gzp 59 47 the the DT cord-209166-1drg5gzp 59 48 containing contain VBG cord-209166-1drg5gzp 59 49 force force NN cord-209166-1drg5gzp 59 50 we -PRON- PRP cord-209166-1drg5gzp 59 51 only only RB cord-209166-1drg5gzp 59 52 consider consider VBP cord-209166-1drg5gzp 59 53 it -PRON- PRP cord-209166-1drg5gzp 59 54 's be VBZ cord-209166-1drg5gzp 59 55 contribution contribution NN cord-209166-1drg5gzp 59 56 along along IN cord-209166-1drg5gzp 59 57 X x NN cord-209166-1drg5gzp 59 58 axis axis NN cord-209166-1drg5gzp 59 59 . . . cord-209166-1drg5gzp 60 1 So so RB cord-209166-1drg5gzp 60 2 the the DT cord-209166-1drg5gzp 60 3 simplified simplified JJ cord-209166-1drg5gzp 60 4 equations equation NNS cord-209166-1drg5gzp 60 5 for for IN cord-209166-1drg5gzp 60 6 potential potential NN cord-209166-1drg5gzp 60 7 and and CC cord-209166-1drg5gzp 60 8 force force NN cord-209166-1drg5gzp 60 9 will will MD cord-209166-1drg5gzp 60 10 be be VB cord-209166-1drg5gzp 60 11 : : : cord-209166-1drg5gzp 60 12 We -PRON- PRP cord-209166-1drg5gzp 60 13 are be VBP cord-209166-1drg5gzp 60 14 calculating calculate VBG cord-209166-1drg5gzp 60 15 for for IN cord-209166-1drg5gzp 60 16 which which WDT cord-209166-1drg5gzp 60 17 angular angular JJ cord-209166-1drg5gzp 60 18 velocity velocity NN cord-209166-1drg5gzp 60 19 ( ( -LRB- cord-209166-1drg5gzp 60 20 ω ω NN cord-209166-1drg5gzp 60 21 ) ) -RRB- cord-209166-1drg5gzp 61 1 the the DT cord-209166-1drg5gzp 61 2 fluid fluid JJ cord-209166-1drg5gzp 61 3 layer layer NN cord-209166-1drg5gzp 61 4 along along IN cord-209166-1drg5gzp 61 5 Z− Z− NNP cord-209166-1drg5gzp 61 6 axis axis NN cord-209166-1drg5gzp 61 7 just just RB cord-209166-1drg5gzp 61 8 touches touch VBZ cord-209166-1drg5gzp 61 9 the the DT cord-209166-1drg5gzp 61 10 surface surface NN cord-209166-1drg5gzp 61 11 of of IN cord-209166-1drg5gzp 61 12 the the DT cord-209166-1drg5gzp 61 13 metal metal NN cord-209166-1drg5gzp 61 14 sphere sphere NN cord-209166-1drg5gzp 61 15 . . . cord-209166-1drg5gzp 62 1 To to TO cord-209166-1drg5gzp 62 2 find find VB cord-209166-1drg5gzp 62 3 the the DT cord-209166-1drg5gzp 62 4 required require VBN cord-209166-1drg5gzp 62 5 angular angular JJ cord-209166-1drg5gzp 62 6 velocity velocity NN cord-209166-1drg5gzp 62 7 we -PRON- PRP cord-209166-1drg5gzp 62 8 have have VBP cord-209166-1drg5gzp 62 9 to to TO cord-209166-1drg5gzp 62 10 use use VB cord-209166-1drg5gzp 62 11 Conservation Conservation NNP cord-209166-1drg5gzp 62 12 of of IN cord-209166-1drg5gzp 62 13 Energy Energy NNP cord-209166-1drg5gzp 62 14 . . . cord-209166-1drg5gzp 63 1 Now now RB cord-209166-1drg5gzp 63 2 since since IN cord-209166-1drg5gzp 63 3 the the DT cord-209166-1drg5gzp 63 4 rotation rotation NN cord-209166-1drg5gzp 63 5 of of IN cord-209166-1drg5gzp 63 6 the the DT cord-209166-1drg5gzp 63 7 complete complete JJ cord-209166-1drg5gzp 63 8 system system NN cord-209166-1drg5gzp 63 9 is be VBZ cord-209166-1drg5gzp 63 10 resulting result VBG cord-209166-1drg5gzp 63 11 in in IN cord-209166-1drg5gzp 63 12 the the DT cord-209166-1drg5gzp 63 13 change change NN cord-209166-1drg5gzp 63 14 in in IN cord-209166-1drg5gzp 63 15 the the DT cord-209166-1drg5gzp 63 16 shape shape NN cord-209166-1drg5gzp 63 17 of of IN cord-209166-1drg5gzp 63 18 the the DT cord-209166-1drg5gzp 63 19 surface surface NN cord-209166-1drg5gzp 63 20 , , , cord-209166-1drg5gzp 63 21 hence hence RB cord-209166-1drg5gzp 63 22 total total JJ cord-209166-1drg5gzp 63 23 rotational rotational JJ cord-209166-1drg5gzp 63 24 energy energy NN cord-209166-1drg5gzp 63 25 can can MD cord-209166-1drg5gzp 63 26 be be VB cord-209166-1drg5gzp 63 27 considered consider VBN cord-209166-1drg5gzp 63 28 to to TO cord-209166-1drg5gzp 63 29 be be VB cord-209166-1drg5gzp 63 30 transferred transfer VBN cord-209166-1drg5gzp 63 31 to to IN cord-209166-1drg5gzp 63 32 the the DT cord-209166-1drg5gzp 63 33 overall overall JJ cord-209166-1drg5gzp 63 34 change change NN cord-209166-1drg5gzp 63 35 in in IN cord-209166-1drg5gzp 63 36 the the DT cord-209166-1drg5gzp 63 37 surface surface NN cord-209166-1drg5gzp 63 38 energy energy NN cord-209166-1drg5gzp 63 39 due due JJ cord-209166-1drg5gzp 63 40 to to IN cord-209166-1drg5gzp 63 41 changed change VBN cord-209166-1drg5gzp 63 42 shape shape NN cord-209166-1drg5gzp 63 43 of of IN cord-209166-1drg5gzp 63 44 the the DT cord-209166-1drg5gzp 63 45 fluid fluid JJ cord-209166-1drg5gzp 63 46 layer layer NN cord-209166-1drg5gzp 63 47 . . . cord-209166-1drg5gzp 64 1 Let let VB cord-209166-1drg5gzp 64 2 γ γ NNP cord-209166-1drg5gzp 64 3 wa wa NNP cord-209166-1drg5gzp 64 4 and and CC cord-209166-1drg5gzp 64 5 γ γ NNP cord-209166-1drg5gzp 64 6 ws ws NNPS cord-209166-1drg5gzp 64 7 be be VB cord-209166-1drg5gzp 64 8 the the DT cord-209166-1drg5gzp 64 9 interfacial interfacial JJ cord-209166-1drg5gzp 64 10 energy energy NN cord-209166-1drg5gzp 64 11 between between IN cord-209166-1drg5gzp 64 12 water water NN cord-209166-1drg5gzp 64 13 layer layer NN cord-209166-1drg5gzp 64 14 and and CC cord-209166-1drg5gzp 64 15 the the DT cord-209166-1drg5gzp 64 16 gas gas NN cord-209166-1drg5gzp 64 17 or or CC cord-209166-1drg5gzp 64 18 air air NN cord-209166-1drg5gzp 64 19 present present JJ cord-209166-1drg5gzp 64 20 outside outside IN cord-209166-1drg5gzp 64 21 and and CC cord-209166-1drg5gzp 64 22 between between IN cord-209166-1drg5gzp 64 23 water water NN cord-209166-1drg5gzp 64 24 layer layer NN cord-209166-1drg5gzp 64 25 and and CC cord-209166-1drg5gzp 64 26 solid solid JJ cord-209166-1drg5gzp 64 27 metal metal NN cord-209166-1drg5gzp 64 28 surface surface NN cord-209166-1drg5gzp 64 29 respectively respectively RB cord-209166-1drg5gzp 64 30 . . . cord-209166-1drg5gzp 65 1 Let let VB cord-209166-1drg5gzp 65 2 ∆E ∆E NNP cord-209166-1drg5gzp 65 3 1 1 CD cord-209166-1drg5gzp 65 4 and and CC cord-209166-1drg5gzp 65 5 ∆E ∆E NNP cord-209166-1drg5gzp 65 6 2 2 CD cord-209166-1drg5gzp 65 7 be be VBP cord-209166-1drg5gzp 65 8 the the DT cord-209166-1drg5gzp 65 9 initial initial JJ cord-209166-1drg5gzp 65 10 and and CC cord-209166-1drg5gzp 65 11 final final JJ cord-209166-1drg5gzp 65 12 surface surface NN cord-209166-1drg5gzp 65 13 energies energy NNS cord-209166-1drg5gzp 65 14 of of IN cord-209166-1drg5gzp 65 15 the the DT cord-209166-1drg5gzp 65 16 system system NN cord-209166-1drg5gzp 65 17 respectively respectively RB cord-209166-1drg5gzp 65 18 . . . cord-209166-1drg5gzp 66 1 Also also RB cord-209166-1drg5gzp 66 2 , , , cord-209166-1drg5gzp 66 3 let let VB cord-209166-1drg5gzp 66 4 the the DT cord-209166-1drg5gzp 66 5 initial initial JJ cord-209166-1drg5gzp 66 6 and and CC cord-209166-1drg5gzp 66 7 final final JJ cord-209166-1drg5gzp 66 8 surface surface NN cord-209166-1drg5gzp 66 9 areas area NNS cord-209166-1drg5gzp 66 10 of of IN cord-209166-1drg5gzp 66 11 the the DT cord-209166-1drg5gzp 66 12 fluid fluid JJ cord-209166-1drg5gzp 66 13 layer layer NN cord-209166-1drg5gzp 66 14 be be VB cord-209166-1drg5gzp 66 15 S S NNP cord-209166-1drg5gzp 66 16 and and CC cord-209166-1drg5gzp 66 17 S S NNP cord-209166-1drg5gzp 66 18 respectively respectively RB cord-209166-1drg5gzp 66 19 . . . cord-209166-1drg5gzp 67 1 Then then RB cord-209166-1drg5gzp 67 2 we -PRON- PRP cord-209166-1drg5gzp 67 3 can can MD cord-209166-1drg5gzp 67 4 write write VB cord-209166-1drg5gzp 67 5 : : : cord-209166-1drg5gzp 68 1 For for IN cord-209166-1drg5gzp 68 2 conserving conserve VBG cord-209166-1drg5gzp 68 3 total total JJ cord-209166-1drg5gzp 68 4 energy energy NN cord-209166-1drg5gzp 68 5 of of IN cord-209166-1drg5gzp 68 6 the the DT cord-209166-1drg5gzp 68 7 system system NN cord-209166-1drg5gzp 68 8 , , , cord-209166-1drg5gzp 68 9 we -PRON- PRP cord-209166-1drg5gzp 68 10 can can MD cord-209166-1drg5gzp 68 11 say say VB cord-209166-1drg5gzp 68 12 that that IN cord-209166-1drg5gzp 68 13 total total JJ cord-209166-1drg5gzp 68 14 energy energy NN cord-209166-1drg5gzp 68 15 available available JJ cord-209166-1drg5gzp 68 16 initially initially RB cord-209166-1drg5gzp 68 17 will will MD cord-209166-1drg5gzp 68 18 be be VB cord-209166-1drg5gzp 68 19 equal equal JJ cord-209166-1drg5gzp 68 20 to to IN cord-209166-1drg5gzp 68 21 the the DT cord-209166-1drg5gzp 68 22 total total JJ cord-209166-1drg5gzp 68 23 energy energy NN cord-209166-1drg5gzp 68 24 available available JJ cord-209166-1drg5gzp 68 25 finally finally RB cord-209166-1drg5gzp 68 26 with with IN cord-209166-1drg5gzp 68 27 the the DT cord-209166-1drg5gzp 68 28 system system NN cord-209166-1drg5gzp 68 29 . . . cord-209166-1drg5gzp 69 1 Hence hence RB cord-209166-1drg5gzp 69 2 we -PRON- PRP cord-209166-1drg5gzp 69 3 can can MD cord-209166-1drg5gzp 69 4 write write VB cord-209166-1drg5gzp 69 5 : : : cord-209166-1drg5gzp 70 1 Change change VB cord-209166-1drg5gzp 70 2 in in IN cord-209166-1drg5gzp 70 3 Rotational Rotational NNP cord-209166-1drg5gzp 70 4 Kinetic Kinetic NNP cord-209166-1drg5gzp 70 5 Energy Energy NNP cord-209166-1drg5gzp 70 6 = = SYM cord-209166-1drg5gzp 70 7 Change change NN cord-209166-1drg5gzp 70 8 in in IN cord-209166-1drg5gzp 70 9 Surface Surface NNP cord-209166-1drg5gzp 70 10 Energy Energy NNP cord-209166-1drg5gzp 71 1 Now now RB cord-209166-1drg5gzp 71 2 , , , cord-209166-1drg5gzp 71 3 Moment moment NN cord-209166-1drg5gzp 71 4 of of IN cord-209166-1drg5gzp 71 5 Inertia Inertia NNP cord-209166-1drg5gzp 71 6 ( ( -LRB- cord-209166-1drg5gzp 71 7 I -PRON- PRP cord-209166-1drg5gzp 71 8 net net NN cord-209166-1drg5gzp 71 9 ) ) -RRB- cord-209166-1drg5gzp 71 10 of of IN cord-209166-1drg5gzp 71 11 the the DT cord-209166-1drg5gzp 71 12 overall overall JJ cord-209166-1drg5gzp 71 13 system system NN cord-209166-1drg5gzp 71 14 can can MD cord-209166-1drg5gzp 71 15 be be VB cord-209166-1drg5gzp 71 16 divided divide VBN cord-209166-1drg5gzp 71 17 into into IN cord-209166-1drg5gzp 71 18 three three CD cord-209166-1drg5gzp 71 19 parts part NNS cord-209166-1drg5gzp 71 20 , , , cord-209166-1drg5gzp 71 21 i.e. i.e. FW cord-209166-1drg5gzp 71 22 , , , cord-209166-1drg5gzp 71 23 moment moment NN cord-209166-1drg5gzp 71 24 of of IN cord-209166-1drg5gzp 71 25 inertia inertia NN cord-209166-1drg5gzp 71 26 of of IN cord-209166-1drg5gzp 71 27 the the DT cord-209166-1drg5gzp 71 28 overall overall JJ cord-209166-1drg5gzp 71 29 spheroid(I spheroid(I NNP cord-209166-1drg5gzp 71 30 1 1 CD cord-209166-1drg5gzp 71 31 ) ) -RRB- cord-209166-1drg5gzp 71 32 , , , cord-209166-1drg5gzp 71 33 moment moment NN cord-209166-1drg5gzp 71 34 of of IN cord-209166-1drg5gzp 71 35 inertia inertia NN cord-209166-1drg5gzp 71 36 of of IN cord-209166-1drg5gzp 71 37 the the DT cord-209166-1drg5gzp 71 38 cavity cavity NN cord-209166-1drg5gzp 71 39 ( ( -LRB- cord-209166-1drg5gzp 71 40 I i NN cord-209166-1drg5gzp 71 41 2 2 CD cord-209166-1drg5gzp 71 42 ) ) -RRB- cord-209166-1drg5gzp 71 43 ( ( -LRB- cord-209166-1drg5gzp 71 44 which which WDT cord-209166-1drg5gzp 71 45 is be VBZ cord-209166-1drg5gzp 71 46 to to TO cord-209166-1drg5gzp 71 47 be be VB cord-209166-1drg5gzp 71 48 subtracted subtract VBN cord-209166-1drg5gzp 71 49 from from IN cord-209166-1drg5gzp 71 50 that that DT cord-209166-1drg5gzp 71 51 of of IN cord-209166-1drg5gzp 71 52 the the DT cord-209166-1drg5gzp 71 53 spheroid spheroid NN cord-209166-1drg5gzp 71 54 ) ) -RRB- cord-209166-1drg5gzp 71 55 and and CC cord-209166-1drg5gzp 71 56 moment moment NN cord-209166-1drg5gzp 71 57 of of IN cord-209166-1drg5gzp 71 58 inertia inertia NN cord-209166-1drg5gzp 71 59 of of IN cord-209166-1drg5gzp 71 60 the the DT cord-209166-1drg5gzp 71 61 metal metal NN cord-209166-1drg5gzp 71 62 ball ball NN cord-209166-1drg5gzp 71 63 ( ( -LRB- cord-209166-1drg5gzp 71 64 I i NN cord-209166-1drg5gzp 71 65 3 3 CD cord-209166-1drg5gzp 71 66 ) ) -RRB- cord-209166-1drg5gzp 71 67 . . . cord-209166-1drg5gzp 72 1 Hence hence RB cord-209166-1drg5gzp 72 2 we -PRON- PRP cord-209166-1drg5gzp 72 3 can can MD cord-209166-1drg5gzp 72 4 write write VB cord-209166-1drg5gzp 72 5 : : : cord-209166-1drg5gzp 73 1 I -PRON- PRP cord-209166-1drg5gzp 73 2 net net JJ cord-209166-1drg5gzp 73 3 = = NFP cord-209166-1drg5gzp 74 1 I -PRON- PRP cord-209166-1drg5gzp 75 1 1 1 LS cord-209166-1drg5gzp 75 2 − − NN cord-209166-1drg5gzp 76 1 I -PRON- PRP cord-209166-1drg5gzp 76 2 2 2 CD cord-209166-1drg5gzp 77 1 + + CC cord-209166-1drg5gzp 77 2 I i NN cord-209166-1drg5gzp 77 3 3 3 CD cord-209166-1drg5gzp 78 1 Now now RB cord-209166-1drg5gzp 78 2 , , , cord-209166-1drg5gzp 78 3 Therefore therefore RB cord-209166-1drg5gzp 78 4 we -PRON- PRP cord-209166-1drg5gzp 78 5 have have VBP cord-209166-1drg5gzp 78 6 , , , cord-209166-1drg5gzp 78 7 Using use VBG cord-209166-1drg5gzp 78 8 Equation equation NN cord-209166-1drg5gzp 78 9 1 1 CD cord-209166-1drg5gzp 78 10 , , , cord-209166-1drg5gzp 78 11 we -PRON- PRP cord-209166-1drg5gzp 78 12 have have VBP cord-209166-1drg5gzp 78 13 Now now RB cord-209166-1drg5gzp 78 14 the the DT cord-209166-1drg5gzp 78 15 Surface Surface NNP cord-209166-1drg5gzp 78 16 area area NN cord-209166-1drg5gzp 78 17 of of IN cord-209166-1drg5gzp 78 18 the the DT cord-209166-1drg5gzp 78 19 spheroid spheroid NN cord-209166-1drg5gzp 78 20 with with IN cord-209166-1drg5gzp 78 21 equation equation NN cord-209166-1drg5gzp 78 22 Now now RB cord-209166-1drg5gzp 78 23 for for IN cord-209166-1drg5gzp 78 24 our -PRON- PRP$ cord-209166-1drg5gzp 78 25 case case NN cord-209166-1drg5gzp 78 26 we -PRON- PRP cord-209166-1drg5gzp 78 27 have have VBP cord-209166-1drg5gzp 78 28 a a DT cord-209166-1drg5gzp 78 29 = = NN cord-209166-1drg5gzp 79 1 ( ( -LRB- cord-209166-1drg5gzp 79 2 R r NN cord-209166-1drg5gzp 79 3 + + CC cord-209166-1drg5gzp 79 4 m m NN cord-209166-1drg5gzp 79 5 ) ) -RRB- cord-209166-1drg5gzp 79 6 1 1 CD cord-209166-1drg5gzp 79 7 + + CC cord-209166-1drg5gzp 79 8 m m NN cord-209166-1drg5gzp 79 9 R r NN cord-209166-1drg5gzp 79 10 and and CC cord-209166-1drg5gzp 79 11 c c NN cord-209166-1drg5gzp 79 12 = = SYM cord-209166-1drg5gzp 79 13 R r NN cord-209166-1drg5gzp 79 14 , , , cord-209166-1drg5gzp 79 15 Hence hence RB cord-209166-1drg5gzp 79 16 ; ; : cord-209166-1drg5gzp 79 17 So so CC cord-209166-1drg5gzp 79 18 using use VBG cord-209166-1drg5gzp 79 19 the the DT cord-209166-1drg5gzp 79 20 value value NN cord-209166-1drg5gzp 79 21 of of IN cord-209166-1drg5gzp 79 22 S s NN cord-209166-1drg5gzp 80 1 and and CC cord-209166-1drg5gzp 80 2 I -PRON- PRP cord-209166-1drg5gzp 80 3 net net VBP cord-209166-1drg5gzp 81 1 we -PRON- PRP cord-209166-1drg5gzp 81 2 can can MD cord-209166-1drg5gzp 81 3 find find VB cord-209166-1drg5gzp 81 4 the the DT cord-209166-1drg5gzp 81 5 value value NN cord-209166-1drg5gzp 81 6 of of IN cord-209166-1drg5gzp 81 7 ω ω NN cord-209166-1drg5gzp 81 8 as as IN cord-209166-1drg5gzp 81 9 : : : cord-209166-1drg5gzp 82 1 Now now RB cord-209166-1drg5gzp 82 2 for for IN cord-209166-1drg5gzp 82 3 m m XX cord-209166-1drg5gzp 82 4 < < XX cord-209166-1drg5gzp 82 5 < < XX cord-209166-1drg5gzp 82 6 R r NN cord-209166-1drg5gzp 82 7 ; ; : cord-209166-1drg5gzp 82 8 we -PRON- PRP cord-209166-1drg5gzp 82 9 can can MD cord-209166-1drg5gzp 82 10 approximate approximate VB cord-209166-1drg5gzp 82 11 the the DT cord-209166-1drg5gzp 82 12 value value NN cord-209166-1drg5gzp 82 13 of of IN cord-209166-1drg5gzp 82 14 ω ω NN cord-209166-1drg5gzp 82 15 by by IN cord-209166-1drg5gzp 82 16 using use VBG cord-209166-1drg5gzp 82 17 Taylor Taylor NNP cord-209166-1drg5gzp 82 18 's 's POS cord-209166-1drg5gzp 82 19 Series Series NNP cord-209166-1drg5gzp 82 20 [ [ -LRB- cord-209166-1drg5gzp 82 21 5 5 CD cord-209166-1drg5gzp 82 22 ] ] -RRB- cord-209166-1drg5gzp 82 23 up up RB cord-209166-1drg5gzp 82 24 to to IN cord-209166-1drg5gzp 82 25 O(1 O(1 NNP cord-209166-1drg5gzp 82 26 ) ) -RRB- cord-209166-1drg5gzp 82 27 and and CC cord-209166-1drg5gzp 82 28 from from IN cord-209166-1drg5gzp 82 29 that that DT cord-209166-1drg5gzp 82 30 we -PRON- PRP cord-209166-1drg5gzp 82 31 get get VBP cord-209166-1drg5gzp 82 32 the the DT cord-209166-1drg5gzp 82 33 expression expression NN cord-209166-1drg5gzp 82 34 of of IN cord-209166-1drg5gzp 82 35 ω ω NN cord-209166-1drg5gzp 82 36 as as IN cord-209166-1drg5gzp 82 37 : : : cord-209166-1drg5gzp 82 38 The the DT cord-209166-1drg5gzp 82 39 simplified simplified JJ cord-209166-1drg5gzp 82 40 expression expression NN cord-209166-1drg5gzp 82 41 for for IN cord-209166-1drg5gzp 82 42 Force Force NNP cord-209166-1drg5gzp 82 43 in in IN cord-209166-1drg5gzp 82 44 equation equation NN cord-209166-1drg5gzp 82 45 9 9 CD cord-209166-1drg5gzp 82 46 can can MD cord-209166-1drg5gzp 82 47 be be VB cord-209166-1drg5gzp 82 48 plotted plot VBN cord-209166-1drg5gzp 82 49 with with IN cord-209166-1drg5gzp 82 50 respect respect NN cord-209166-1drg5gzp 82 51 to to IN cord-209166-1drg5gzp 82 52 distance distance NN cord-209166-1drg5gzp 82 53 measured measure VBN cord-209166-1drg5gzp 82 54 along along IN cord-209166-1drg5gzp 82 55 X x NN cord-209166-1drg5gzp 82 56 - - NN cord-209166-1drg5gzp 82 57 axis axis NN cord-209166-1drg5gzp 82 58 as as IN cord-209166-1drg5gzp 82 59 shown show VBN cord-209166-1drg5gzp 82 60 in in IN cord-209166-1drg5gzp 82 61 Figure Figure NNP cord-209166-1drg5gzp 82 62 4 4 CD cord-209166-1drg5gzp 82 63 . . . cord-209166-1drg5gzp 83 1 Now now RB cord-209166-1drg5gzp 83 2 as as IN cord-209166-1drg5gzp 83 3 we -PRON- PRP cord-209166-1drg5gzp 83 4 can can MD cord-209166-1drg5gzp 83 5 see see VB cord-209166-1drg5gzp 83 6 that that IN cord-209166-1drg5gzp 83 7 we -PRON- PRP cord-209166-1drg5gzp 83 8 had have VBD cord-209166-1drg5gzp 83 9 restricted restrict VBN cord-209166-1drg5gzp 83 10 the the DT cord-209166-1drg5gzp 83 11 plot plot NN cord-209166-1drg5gzp 83 12 of of IN cord-209166-1drg5gzp 83 13 F(x F(x NNP cord-209166-1drg5gzp 83 14 ) ) -RRB- cord-209166-1drg5gzp 83 15 from from IN cord-209166-1drg5gzp 83 16 the the DT cord-209166-1drg5gzp 83 17 radius radius NN cord-209166-1drg5gzp 83 18 of of IN cord-209166-1drg5gzp 83 19 the the DT cord-209166-1drg5gzp 83 20 metal metal NN cord-209166-1drg5gzp 83 21 sphere sphere NN cord-209166-1drg5gzp 83 22 R r NN cord-209166-1drg5gzp 83 23 , , , cord-209166-1drg5gzp 83 24 up up IN cord-209166-1drg5gzp 83 25 to to IN cord-209166-1drg5gzp 83 26 the the DT cord-209166-1drg5gzp 83 27 semi semi JJ cord-209166-1drg5gzp 83 28 - - JJ cord-209166-1drg5gzp 83 29 major major JJ cord-209166-1drg5gzp 83 30 axis axis NN cord-209166-1drg5gzp 83 31 along along IN cord-209166-1drg5gzp 83 32 X x NN cord-209166-1drg5gzp 83 33 axis axis NN cord-209166-1drg5gzp 83 34 or or CC cord-209166-1drg5gzp 83 35 Y Y NNP cord-209166-1drg5gzp 83 36 axis axis NN cord-209166-1drg5gzp 83 37 , , , cord-209166-1drg5gzp 83 38 a a DT cord-209166-1drg5gzp 83 39 = = NN cord-209166-1drg5gzp 84 1 ( ( -LRB- cord-209166-1drg5gzp 84 2 R r NN cord-209166-1drg5gzp 84 3 + + CC cord-209166-1drg5gzp 84 4 m m NN cord-209166-1drg5gzp 84 5 ) ) -RRB- cord-209166-1drg5gzp 84 6 1 1 CD cord-209166-1drg5gzp 84 7 + + CC cord-209166-1drg5gzp 84 8 m m NN cord-209166-1drg5gzp 84 9 R r NN cord-209166-1drg5gzp 84 10 , , , cord-209166-1drg5gzp 84 11 which which WDT cord-209166-1drg5gzp 84 12 corresponds correspond VBZ cord-209166-1drg5gzp 84 13 to to IN cord-209166-1drg5gzp 84 14 the the DT cord-209166-1drg5gzp 84 15 force force NN cord-209166-1drg5gzp 84 16 values value NNS cord-209166-1drg5gzp 84 17 F F NNP cord-209166-1drg5gzp 84 18 max max NNP cord-209166-1drg5gzp 84 19 and and CC cord-209166-1drg5gzp 84 20 F F NNP cord-209166-1drg5gzp 84 21 min min NNP cord-209166-1drg5gzp 84 22 respectively respectively RB cord-209166-1drg5gzp 84 23 . . . cord-209166-1drg5gzp 85 1 The the DT cord-209166-1drg5gzp 85 2 restriction restriction NN cord-209166-1drg5gzp 85 3 comes come VBZ cord-209166-1drg5gzp 85 4 with with IN cord-209166-1drg5gzp 85 5 the the DT cord-209166-1drg5gzp 85 6 reason reason NN cord-209166-1drg5gzp 85 7 that that IN cord-209166-1drg5gzp 85 8 the the DT cord-209166-1drg5gzp 85 9 considered consider VBN cord-209166-1drg5gzp 85 10 containing contain VBG cord-209166-1drg5gzp 85 11 force force NN cord-209166-1drg5gzp 85 12 is be VBZ cord-209166-1drg5gzp 85 13 limited limit VBN cord-209166-1drg5gzp 85 14 to to IN cord-209166-1drg5gzp 85 15 a a DT cord-209166-1drg5gzp 85 16 particular particular JJ cord-209166-1drg5gzp 85 17 value value NN cord-209166-1drg5gzp 85 18 of of IN cord-209166-1drg5gzp 85 19 x x NN cord-209166-1drg5gzp 85 20 beyond beyond IN cord-209166-1drg5gzp 85 21 which which WDT cord-209166-1drg5gzp 85 22 , , , cord-209166-1drg5gzp 85 23 the the DT cord-209166-1drg5gzp 85 24 magnitude magnitude NN cord-209166-1drg5gzp 85 25 of of IN cord-209166-1drg5gzp 85 26 force force NN cord-209166-1drg5gzp 85 27 becomes become VBZ cord-209166-1drg5gzp 85 28 inconsistent inconsistent JJ cord-209166-1drg5gzp 85 29 with with IN cord-209166-1drg5gzp 85 30 the the DT cord-209166-1drg5gzp 85 31 physical physical JJ cord-209166-1drg5gzp 85 32 system system NN cord-209166-1drg5gzp 85 33 as as IN cord-209166-1drg5gzp 85 34 fluid fluid NN cord-209166-1drg5gzp 85 35 is be VBZ cord-209166-1drg5gzp 85 36 present present JJ cord-209166-1drg5gzp 85 37 from from IN cord-209166-1drg5gzp 85 38 the the DT cord-209166-1drg5gzp 85 39 surface surface NN cord-209166-1drg5gzp 85 40 of of IN cord-209166-1drg5gzp 85 41 the the DT cord-209166-1drg5gzp 85 42 metal metal NN cord-209166-1drg5gzp 85 43 sphere sphere NN cord-209166-1drg5gzp 85 44 up up IN cord-209166-1drg5gzp 85 45 to to IN cord-209166-1drg5gzp 85 46 the the DT cord-209166-1drg5gzp 85 47 liquid liquid NN cord-209166-1drg5gzp 85 48 and and CC cord-209166-1drg5gzp 85 49 air air NN cord-209166-1drg5gzp 85 50 interface interface NN cord-209166-1drg5gzp 85 51 . . . cord-209166-1drg5gzp 85 52 _SP cord-209166-1drg5gzp 86 1 The the DT cord-209166-1drg5gzp 86 2 force force NN cord-209166-1drg5gzp 86 3 at at IN cord-209166-1drg5gzp 86 4 x x SYM cord-209166-1drg5gzp 86 5 = = NFP cord-209166-1drg5gzp 86 6 a a NN cord-209166-1drg5gzp 86 7 is be VBZ cord-209166-1drg5gzp 86 8 given give VBN cord-209166-1drg5gzp 86 9 by by IN cord-209166-1drg5gzp 86 10 F F NNP cord-209166-1drg5gzp 86 11 min min NN cord-209166-1drg5gzp 86 12 = = SYM cord-209166-1drg5gzp 86 13 F(a F(a NNP cord-209166-1drg5gzp 86 14 ) ) -RRB- cord-209166-1drg5gzp 86 15 = = NFP cord-209166-1drg5gzp 87 1 2a 2a LS cord-209166-1drg5gzp 87 2 2 2 CD cord-209166-1drg5gzp 87 3 γ γ NN cord-209166-1drg5gzp 87 4 ρ ρ NN cord-209166-1drg5gzp 87 5 . . . cord-209166-1drg5gzp 88 1 This this DT cord-209166-1drg5gzp 88 2 agrees agree VBZ cord-209166-1drg5gzp 88 3 with with IN cord-209166-1drg5gzp 88 4 the the DT cord-209166-1drg5gzp 88 5 fact fact NN cord-209166-1drg5gzp 88 6 that that IN cord-209166-1drg5gzp 88 7 for for IN cord-209166-1drg5gzp 88 8 the the DT cord-209166-1drg5gzp 88 9 system system NN cord-209166-1drg5gzp 88 10 being be VBG cord-209166-1drg5gzp 88 11 static static JJ cord-209166-1drg5gzp 88 12 or or CC cord-209166-1drg5gzp 88 13 without without IN cord-209166-1drg5gzp 88 14 any any DT cord-209166-1drg5gzp 88 15 rotation rotation NN cord-209166-1drg5gzp 88 16 , , , cord-209166-1drg5gzp 88 17 this this DT cord-209166-1drg5gzp 88 18 force force NN cord-209166-1drg5gzp 88 19 is be VBZ cord-209166-1drg5gzp 88 20 responsible responsible JJ cord-209166-1drg5gzp 88 21 for for IN cord-209166-1drg5gzp 88 22 bringing bring VBG cord-209166-1drg5gzp 88 23 the the DT cord-209166-1drg5gzp 88 24 surface surface NN cord-209166-1drg5gzp 88 25 of of IN cord-209166-1drg5gzp 88 26 the the DT cord-209166-1drg5gzp 88 27 liquid liquid NN cord-209166-1drg5gzp 88 28 to to IN cord-209166-1drg5gzp 88 29 the the DT cord-209166-1drg5gzp 88 30 equilibrium equilibrium NN cord-209166-1drg5gzp 88 31 position position NN cord-209166-1drg5gzp 88 32 , , , cord-209166-1drg5gzp 88 33 i.e. i.e. FW cord-209166-1drg5gzp 88 34 into into IN cord-209166-1drg5gzp 88 35 the the DT cord-209166-1drg5gzp 88 36 spherical spherical JJ cord-209166-1drg5gzp 88 37 shape shape NN cord-209166-1drg5gzp 88 38 . . . cord-209166-1drg5gzp 89 1 Now now RB cord-209166-1drg5gzp 89 2 during during IN cord-209166-1drg5gzp 89 3 rotation rotation NN cord-209166-1drg5gzp 89 4 , , , cord-209166-1drg5gzp 89 5 this this DT cord-209166-1drg5gzp 89 6 force force NN cord-209166-1drg5gzp 89 7 is be VBZ cord-209166-1drg5gzp 89 8 balanced balance VBN cord-209166-1drg5gzp 89 9 by by IN cord-209166-1drg5gzp 89 10 the the DT cord-209166-1drg5gzp 89 11 centrifugal centrifugal JJ cord-209166-1drg5gzp 89 12 force force NN cord-209166-1drg5gzp 89 13 acting act VBG cord-209166-1drg5gzp 89 14 per per IN cord-209166-1drg5gzp 89 15 unit unit NN cord-209166-1drg5gzp 89 16 mass mass NN cord-209166-1drg5gzp 89 17 along along IN cord-209166-1drg5gzp 89 18 the the DT cord-209166-1drg5gzp 89 19 X x NN cord-209166-1drg5gzp 89 20 direction direction NN cord-209166-1drg5gzp 89 21 . . . cord-209166-1drg5gzp 90 1 Using use VBG cord-209166-1drg5gzp 90 2 this this DT cord-209166-1drg5gzp 90 3 concept concept NN cord-209166-1drg5gzp 90 4 we -PRON- PRP cord-209166-1drg5gzp 90 5 can can MD cord-209166-1drg5gzp 90 6 find find VB cord-209166-1drg5gzp 90 7 a a DT cord-209166-1drg5gzp 90 8 bound bind VBN cord-209166-1drg5gzp 90 9 on on IN cord-209166-1drg5gzp 90 10 the the DT cord-209166-1drg5gzp 90 11 angular angular JJ cord-209166-1drg5gzp 90 12 velocity velocity NN cord-209166-1drg5gzp 90 13 ( ( -LRB- cord-209166-1drg5gzp 90 14 ω ω NN cord-209166-1drg5gzp 90 15 ) ) -RRB- cord-209166-1drg5gzp 90 16 for for IN cord-209166-1drg5gzp 90 17 which which WDT cord-209166-1drg5gzp 90 18 the the DT cord-209166-1drg5gzp 90 19 water water NN cord-209166-1drg5gzp 90 20 layer layer NN cord-209166-1drg5gzp 90 21 remains remain VBZ cord-209166-1drg5gzp 90 22 in in IN cord-209166-1drg5gzp 90 23 shape shape NN cord-209166-1drg5gzp 90 24 of of IN cord-209166-1drg5gzp 90 25 the the DT cord-209166-1drg5gzp 90 26 spheroid spheroid NN cord-209166-1drg5gzp 90 27 without without IN cord-209166-1drg5gzp 90 28 spilling spill VBG cord-209166-1drg5gzp 90 29 out out RP cord-209166-1drg5gzp 90 30 from from IN cord-209166-1drg5gzp 90 31 the the DT cord-209166-1drg5gzp 90 32 system system NN cord-209166-1drg5gzp 90 33 . . . cord-209166-1drg5gzp 91 1 Now now RB cord-209166-1drg5gzp 91 2 if if IN cord-209166-1drg5gzp 91 3 we -PRON- PRP cord-209166-1drg5gzp 91 4 give give VBP cord-209166-1drg5gzp 91 5 ω ω NN cord-209166-1drg5gzp 91 6 > > XX cord-209166-1drg5gzp 91 7 2aγ 2aγ NN cord-209166-1drg5gzp 91 8 ρ ρ NNP cord-209166-1drg5gzp 91 9 , , , cord-209166-1drg5gzp 91 10 the the DT cord-209166-1drg5gzp 91 11 water water NN cord-209166-1drg5gzp 91 12 will will MD cord-209166-1drg5gzp 91 13 start start VB cord-209166-1drg5gzp 91 14 spilling spill VBG cord-209166-1drg5gzp 91 15 out out RP cord-209166-1drg5gzp 91 16 from from IN cord-209166-1drg5gzp 91 17 the the DT cord-209166-1drg5gzp 91 18 outer outer JJ cord-209166-1drg5gzp 91 19 surface surface NN cord-209166-1drg5gzp 91 20 as as IN cord-209166-1drg5gzp 91 21 the the DT cord-209166-1drg5gzp 91 22 force force NN cord-209166-1drg5gzp 91 23 at at IN cord-209166-1drg5gzp 91 24 the the DT cord-209166-1drg5gzp 91 25 boundary boundary NN cord-209166-1drg5gzp 91 26 is be VBZ cord-209166-1drg5gzp 91 27 minimum minimum JJ cord-209166-1drg5gzp 91 28 . . . cord-209166-1drg5gzp 92 1 Similarly similarly RB cord-209166-1drg5gzp 92 2 , , , cord-209166-1drg5gzp 92 3 with with IN cord-209166-1drg5gzp 92 4 same same JJ cord-209166-1drg5gzp 92 5 conditions condition NNS cord-209166-1drg5gzp 92 6 , , , cord-209166-1drg5gzp 92 7 we -PRON- PRP cord-209166-1drg5gzp 92 8 can can MD cord-209166-1drg5gzp 92 9 define define VB cord-209166-1drg5gzp 92 10 the the DT cord-209166-1drg5gzp 92 11 containing containing JJ cord-209166-1drg5gzp 92 12 potential potential NN cord-209166-1drg5gzp 92 13 of of IN cord-209166-1drg5gzp 92 14 the the DT cord-209166-1drg5gzp 92 15 system system NN cord-209166-1drg5gzp 92 16 along along IN cord-209166-1drg5gzp 92 17 X x NN cord-209166-1drg5gzp 92 18 direction direction NN cord-209166-1drg5gzp 92 19 from from IN cord-209166-1drg5gzp 92 20 radius radius NN cord-209166-1drg5gzp 92 21 R r NN cord-209166-1drg5gzp 92 22 to to IN cord-209166-1drg5gzp 92 23 the the DT cord-209166-1drg5gzp 92 24 value value NN cord-209166-1drg5gzp 92 25 a a DT cord-209166-1drg5gzp 92 26 as as IN cord-209166-1drg5gzp 92 27 shown show VBN cord-209166-1drg5gzp 92 28 in in IN cord-209166-1drg5gzp 92 29 Figure figure NN cord-209166-1drg5gzp 92 30 5 5 CD cord-209166-1drg5gzp 92 31 . . . cord-209166-1drg5gzp 93 1 The the DT cord-209166-1drg5gzp 93 2 potential potential JJ cord-209166-1drg5gzp 93 3 trend trend NN cord-209166-1drg5gzp 93 4 also also RB cord-209166-1drg5gzp 93 5 have have VBP cord-209166-1drg5gzp 93 6 physical physical JJ cord-209166-1drg5gzp 93 7 significance significance NN cord-209166-1drg5gzp 93 8 , , , cord-209166-1drg5gzp 93 9 since since IN cord-209166-1drg5gzp 93 10 potential potential NN cord-209166-1drg5gzp 93 11 at at IN cord-209166-1drg5gzp 93 12 the the DT cord-209166-1drg5gzp 93 13 surface surface NN cord-209166-1drg5gzp 93 14 of of IN cord-209166-1drg5gzp 93 15 the the DT cord-209166-1drg5gzp 93 16 spheroid spheroid NN cord-209166-1drg5gzp 93 17 surface surface NN cord-209166-1drg5gzp 93 18 of of IN cord-209166-1drg5gzp 93 19 the the DT cord-209166-1drg5gzp 93 20 liquid liquid NN cord-209166-1drg5gzp 93 21 is be VBZ cord-209166-1drg5gzp 93 22 zero zero CD cord-209166-1drg5gzp 93 23 . . . cord-209166-1drg5gzp 94 1 Now now RB cord-209166-1drg5gzp 94 2 with with IN cord-209166-1drg5gzp 94 3 regards regard NNS cord-209166-1drg5gzp 94 4 to to IN cord-209166-1drg5gzp 94 5 the the DT cord-209166-1drg5gzp 94 6 F F NNP cord-209166-1drg5gzp 94 7 max max NNP cord-209166-1drg5gzp 94 8 , , , cord-209166-1drg5gzp 94 9 this this DT cord-209166-1drg5gzp 94 10 force force NN cord-209166-1drg5gzp 94 11 is be VBZ cord-209166-1drg5gzp 94 12 balanced balance VBN cord-209166-1drg5gzp 94 13 by by IN cord-209166-1drg5gzp 94 14 the the DT cord-209166-1drg5gzp 94 15 surface surface NN cord-209166-1drg5gzp 94 16 of of IN cord-209166-1drg5gzp 94 17 the the DT cord-209166-1drg5gzp 94 18 metal metal NN cord-209166-1drg5gzp 94 19 sphere sphere NN cord-209166-1drg5gzp 94 20 , , , cord-209166-1drg5gzp 94 21 since since IN cord-209166-1drg5gzp 94 22 the the DT cord-209166-1drg5gzp 94 23 metal metal NN cord-209166-1drg5gzp 94 24 sphere sphere NN cord-209166-1drg5gzp 94 25 is be VBZ cord-209166-1drg5gzp 94 26 rigid rigid JJ cord-209166-1drg5gzp 94 27 and and CC cord-209166-1drg5gzp 94 28 is be VBZ cord-209166-1drg5gzp 94 29 not not RB cord-209166-1drg5gzp 94 30 deformable deformable JJ cord-209166-1drg5gzp 94 31 . . . cord-209166-1drg5gzp 95 1 We -PRON- PRP cord-209166-1drg5gzp 95 2 are be VBP cord-209166-1drg5gzp 95 3 able able JJ cord-209166-1drg5gzp 95 4 to to TO cord-209166-1drg5gzp 95 5 highlight highlight VB cord-209166-1drg5gzp 95 6 certain certain JJ cord-209166-1drg5gzp 95 7 points point NNS cord-209166-1drg5gzp 95 8 which which WDT cord-209166-1drg5gzp 95 9 may may MD cord-209166-1drg5gzp 95 10 not not RB cord-209166-1drg5gzp 95 11 seem seem VB cord-209166-1drg5gzp 95 12 possible possible JJ cord-209166-1drg5gzp 95 13 to to TO cord-209166-1drg5gzp 95 14 replicate replicate VB cord-209166-1drg5gzp 95 15 on on IN cord-209166-1drg5gzp 95 16 earthly earthly JJ cord-209166-1drg5gzp 95 17 conditions condition NNS cord-209166-1drg5gzp 95 18 , , , cord-209166-1drg5gzp 95 19 by by IN cord-209166-1drg5gzp 95 20 removing remove VBG cord-209166-1drg5gzp 95 21 effects effect NNS cord-209166-1drg5gzp 95 22 on on IN cord-209166-1drg5gzp 95 23 gravity gravity NN cord-209166-1drg5gzp 95 24 but but CC cord-209166-1drg5gzp 95 25 keeping keep VBG cord-209166-1drg5gzp 95 26 other other JJ cord-209166-1drg5gzp 95 27 conditions condition NNS cord-209166-1drg5gzp 95 28 around around IN cord-209166-1drg5gzp 95 29 it -PRON- PRP cord-209166-1drg5gzp 95 30 as as IN cord-209166-1drg5gzp 95 31 such such JJ cord-209166-1drg5gzp 95 32 . . . cord-209166-1drg5gzp 96 1 Under under IN cord-209166-1drg5gzp 96 2 theoretical theoretical JJ cord-209166-1drg5gzp 96 3 considerations consideration NNS cord-209166-1drg5gzp 96 4 , , , cord-209166-1drg5gzp 96 5 we -PRON- PRP cord-209166-1drg5gzp 96 6 were be VBD cord-209166-1drg5gzp 96 7 able able JJ cord-209166-1drg5gzp 96 8 to to TO cord-209166-1drg5gzp 96 9 predict predict VB cord-209166-1drg5gzp 96 10 specific specific JJ cord-209166-1drg5gzp 96 11 aspects aspect NNS cord-209166-1drg5gzp 96 12 like like IN cord-209166-1drg5gzp 96 13 how how WRB cord-209166-1drg5gzp 96 14 much much JJ cord-209166-1drg5gzp 96 15 angular angular JJ cord-209166-1drg5gzp 96 16 velocity velocity NN cord-209166-1drg5gzp 96 17 is be VBZ cord-209166-1drg5gzp 96 18 required require VBN cord-209166-1drg5gzp 96 19 in in IN cord-209166-1drg5gzp 96 20 order order NN cord-209166-1drg5gzp 96 21 to to TO cord-209166-1drg5gzp 96 22 get get VB cord-209166-1drg5gzp 96 23 the the DT cord-209166-1drg5gzp 96 24 desired desire VBN cord-209166-1drg5gzp 96 25 shape shape NN cord-209166-1drg5gzp 96 26 of of IN cord-209166-1drg5gzp 96 27 the the DT cord-209166-1drg5gzp 96 28 liquid liquid JJ cord-209166-1drg5gzp 96 29 drop drop NN cord-209166-1drg5gzp 96 30 with with IN cord-209166-1drg5gzp 96 31 condition condition NN cord-209166-1drg5gzp 96 32 of of IN cord-209166-1drg5gzp 96 33 having have VBG cord-209166-1drg5gzp 96 34 very very RB cord-209166-1drg5gzp 96 35 little little JJ cord-209166-1drg5gzp 96 36 trace trace NN cord-209166-1drg5gzp 96 37 of of IN cord-209166-1drg5gzp 96 38 liquid liquid NN cord-209166-1drg5gzp 96 39 at at IN cord-209166-1drg5gzp 96 40 region region NN cord-209166-1drg5gzp 96 41 along along IN cord-209166-1drg5gzp 96 42 Z Z NNP cord-209166-1drg5gzp 96 43 axis axis NN cord-209166-1drg5gzp 96 44 , , , cord-209166-1drg5gzp 96 45 also also RB cord-209166-1drg5gzp 96 46 called call VBN cord-209166-1drg5gzp 96 47 polar polar JJ cord-209166-1drg5gzp 96 48 region region NN cord-209166-1drg5gzp 96 49 . . . cord-209166-1drg5gzp 97 1 We -PRON- PRP cord-209166-1drg5gzp 97 2 have have VBP cord-209166-1drg5gzp 97 3 to to TO cord-209166-1drg5gzp 97 4 introduce introduce VB cord-209166-1drg5gzp 97 5 the the DT cord-209166-1drg5gzp 97 6 concept concept NN cord-209166-1drg5gzp 97 7 of of IN cord-209166-1drg5gzp 97 8 containing contain VBG cord-209166-1drg5gzp 97 9 force force NN cord-209166-1drg5gzp 97 10 , , , cord-209166-1drg5gzp 97 11 which which WDT cord-209166-1drg5gzp 97 12 is be VBZ cord-209166-1drg5gzp 97 13 other other JJ cord-209166-1drg5gzp 97 14 than than IN cord-209166-1drg5gzp 97 15 gravitational gravitational JJ cord-209166-1drg5gzp 97 16 force force NN cord-209166-1drg5gzp 97 17 present present JJ cord-209166-1drg5gzp 97 18 between between IN cord-209166-1drg5gzp 97 19 the the DT cord-209166-1drg5gzp 97 20 particles particle NNS cord-209166-1drg5gzp 97 21 of of IN cord-209166-1drg5gzp 97 22 the the DT cord-209166-1drg5gzp 97 23 liquid liquid NN cord-209166-1drg5gzp 97 24 and and CC cord-209166-1drg5gzp 97 25 the the DT cord-209166-1drg5gzp 97 26 metal metal NN cord-209166-1drg5gzp 97 27 sphere sphere NN cord-209166-1drg5gzp 97 28 . . . cord-209166-1drg5gzp 98 1 The the DT cord-209166-1drg5gzp 98 2 reason reason NN cord-209166-1drg5gzp 98 3 behind behind IN cord-209166-1drg5gzp 98 4 introduction introduction NN cord-209166-1drg5gzp 98 5 of of IN cord-209166-1drg5gzp 98 6 such such JJ cord-209166-1drg5gzp 98 7 concept concept NN cord-209166-1drg5gzp 98 8 within within IN cord-209166-1drg5gzp 98 9 our -PRON- PRP$ cord-209166-1drg5gzp 98 10 system system NN cord-209166-1drg5gzp 98 11 is be VBZ cord-209166-1drg5gzp 98 12 also also RB cord-209166-1drg5gzp 98 13 explained explain VBN cord-209166-1drg5gzp 98 14 as as IN cord-209166-1drg5gzp 98 15 we -PRON- PRP cord-209166-1drg5gzp 98 16 are be VBP cord-209166-1drg5gzp 98 17 not not RB cord-209166-1drg5gzp 98 18 considering consider VBG cord-209166-1drg5gzp 98 19 very very RB cord-209166-1drg5gzp 98 20 massive massive JJ cord-209166-1drg5gzp 98 21 system system NN cord-209166-1drg5gzp 98 22 like like IN cord-209166-1drg5gzp 98 23 that that DT cord-209166-1drg5gzp 98 24 of of IN cord-209166-1drg5gzp 98 25 a a DT cord-209166-1drg5gzp 98 26 planet planet NN cord-209166-1drg5gzp 98 27 and and CC cord-209166-1drg5gzp 98 28 its -PRON- PRP$ cord-209166-1drg5gzp 98 29 atmospheric atmospheric JJ cord-209166-1drg5gzp 98 30 layer layer NN cord-209166-1drg5gzp 98 31 . . . cord-209166-1drg5gzp 99 1 We -PRON- PRP cord-209166-1drg5gzp 99 2 also also RB cord-209166-1drg5gzp 99 3 explained explain VBD cord-209166-1drg5gzp 99 4 how how WRB cord-209166-1drg5gzp 99 5 the the DT cord-209166-1drg5gzp 99 6 containing contain VBG cord-209166-1drg5gzp 99 7 force force NN cord-209166-1drg5gzp 99 8 is be VBZ cord-209166-1drg5gzp 99 9 helpful helpful JJ cord-209166-1drg5gzp 99 10 for for IN cord-209166-1drg5gzp 99 11 explaining explain VBG cord-209166-1drg5gzp 99 12 the the DT cord-209166-1drg5gzp 99 13 presence presence NN cord-209166-1drg5gzp 99 14 of of IN cord-209166-1drg5gzp 99 15 a a DT cord-209166-1drg5gzp 99 16 potential potential NN cord-209166-1drg5gzp 99 17 , , , cord-209166-1drg5gzp 99 18 which which WDT cord-209166-1drg5gzp 99 19 is be VBZ cord-209166-1drg5gzp 99 20 different different JJ cord-209166-1drg5gzp 99 21 from from IN cord-209166-1drg5gzp 99 22 gravitational gravitational JJ cord-209166-1drg5gzp 99 23 potential potential NN cord-209166-1drg5gzp 99 24 as as IN cord-209166-1drg5gzp 99 25 explained explain VBN cord-209166-1drg5gzp 99 26 in in IN cord-209166-1drg5gzp 99 27 the the DT cord-209166-1drg5gzp 99 28 Maclaurin Maclaurin NNP cord-209166-1drg5gzp 99 29 Spheroid Spheroid NNP cord-209166-1drg5gzp 99 30 [ [ -LRB- cord-209166-1drg5gzp 99 31 2 2 CD cord-209166-1drg5gzp 99 32 ] ] -RRB- cord-209166-1drg5gzp 99 33 . . . cord-209166-1drg5gzp 100 1 If if IN cord-209166-1drg5gzp 100 2 we -PRON- PRP cord-209166-1drg5gzp 100 3 consider consider VBP cord-209166-1drg5gzp 100 4 the the DT cord-209166-1drg5gzp 100 5 gravitational gravitational JJ cord-209166-1drg5gzp 100 6 force force NN cord-209166-1drg5gzp 100 7 and and CC cord-209166-1drg5gzp 100 8 corresponding corresponding JJ cord-209166-1drg5gzp 100 9 gravitational gravitational JJ cord-209166-1drg5gzp 100 10 potential potential NN cord-209166-1drg5gzp 100 11 , , , cord-209166-1drg5gzp 100 12 the the DT cord-209166-1drg5gzp 100 13 expression expression NN cord-209166-1drg5gzp 100 14 for for IN cord-209166-1drg5gzp 100 15 angular angular JJ cord-209166-1drg5gzp 100 16 velocity velocity NN cord-209166-1drg5gzp 100 17 ( ( -LRB- cord-209166-1drg5gzp 100 18 Ω Ω NNP cord-209166-1drg5gzp 100 19 ) ) -RRB- cord-209166-1drg5gzp 100 20 is be VBZ cord-209166-1drg5gzp 100 21 already already RB cord-209166-1drg5gzp 100 22 derived derive VBN cord-209166-1drg5gzp 100 23 as as IN cord-209166-1drg5gzp 100 24 : : : cord-209166-1drg5gzp 100 25 ( ( -LRB- cord-209166-1drg5gzp 100 26 3 3 CD cord-209166-1drg5gzp 100 27 − − NN cord-209166-1drg5gzp 100 28 2e 2e CD cord-209166-1drg5gzp 100 29 2 2 CD cord-209166-1drg5gzp 100 30 ) ) -RRB- cord-209166-1drg5gzp 100 31 sin sin NN cord-209166-1drg5gzp 100 32 −1 −1 NNP cord-209166-1drg5gzp 100 33 e e NNP cord-209166-1drg5gzp 100 34 − − NNP cord-209166-1drg5gzp 100 35 6 6 CD cord-209166-1drg5gzp 100 36 e e NN cord-209166-1drg5gzp 100 37 2 2 CD cord-209166-1drg5gzp 100 38 ( ( -LRB- cord-209166-1drg5gzp 100 39 1 1 CD cord-209166-1drg5gzp 100 40 − − NN cord-209166-1drg5gzp 100 41 e e NN cord-209166-1drg5gzp 100 42 2 2 CD cord-209166-1drg5gzp 100 43 ) ) -RRB- cord-209166-1drg5gzp 100 44 , , . cord-209166-1drg5gzp 101 1 e e LS cord-209166-1drg5gzp 101 2 = = SYM cord-209166-1drg5gzp 101 3 Eccentricity eccentricity NN cord-209166-1drg5gzp 101 4 of of IN cord-209166-1drg5gzp 101 5 the the DT cord-209166-1drg5gzp 101 6 spheroid spheroid NN cord-209166-1drg5gzp 102 1 Further further RB cord-209166-1drg5gzp 102 2 we -PRON- PRP cord-209166-1drg5gzp 102 3 proceed proceed VBP cord-209166-1drg5gzp 102 4 to to TO cord-209166-1drg5gzp 102 5 calculate calculate VB cord-209166-1drg5gzp 102 6 the the DT cord-209166-1drg5gzp 102 7 restriction restriction NN cord-209166-1drg5gzp 102 8 on on IN cord-209166-1drg5gzp 102 9 the the DT cord-209166-1drg5gzp 102 10 angular angular JJ cord-209166-1drg5gzp 102 11 velocity velocity NN cord-209166-1drg5gzp 102 12 beyond beyond IN cord-209166-1drg5gzp 102 13 which which WDT cord-209166-1drg5gzp 102 14 , , , cord-209166-1drg5gzp 102 15 the the DT cord-209166-1drg5gzp 102 16 centrifugal centrifugal JJ cord-209166-1drg5gzp 102 17 force force NN cord-209166-1drg5gzp 102 18 will will MD cord-209166-1drg5gzp 102 19 tend tend VB cord-209166-1drg5gzp 102 20 to to TO cord-209166-1drg5gzp 102 21 spill spill VB cord-209166-1drg5gzp 102 22 the the DT cord-209166-1drg5gzp 102 23 fluid fluid NN cord-209166-1drg5gzp 102 24 from from IN cord-209166-1drg5gzp 102 25 the the DT cord-209166-1drg5gzp 102 26 system system NN cord-209166-1drg5gzp 102 27 , , , cord-209166-1drg5gzp 102 28 leaving leave VBG cord-209166-1drg5gzp 102 29 all all PDT cord-209166-1drg5gzp 102 30 the the DT cord-209166-1drg5gzp 102 31 expressions expression NNS cord-209166-1drg5gzp 102 32 explaining explain VBG cord-209166-1drg5gzp 102 33 the the DT cord-209166-1drg5gzp 102 34 system system NN cord-209166-1drg5gzp 102 35 to to TO cord-209166-1drg5gzp 102 36 be be VB cord-209166-1drg5gzp 102 37 inconsistent inconsistent JJ cord-209166-1drg5gzp 102 38 . . . cord-209166-1drg5gzp 103 1 The the DT cord-209166-1drg5gzp 103 2 system system NN cord-209166-1drg5gzp 103 3 we -PRON- PRP cord-209166-1drg5gzp 103 4 tried try VBD cord-209166-1drg5gzp 103 5 to to TO cord-209166-1drg5gzp 103 6 explain explain VB cord-209166-1drg5gzp 103 7 in in IN cord-209166-1drg5gzp 103 8 the the DT cord-209166-1drg5gzp 103 9 paper paper NN cord-209166-1drg5gzp 103 10 seems seem VBZ cord-209166-1drg5gzp 103 11 to to TO cord-209166-1drg5gzp 103 12 have have VB cord-209166-1drg5gzp 103 13 least least JJS cord-209166-1drg5gzp 103 14 amount amount NN cord-209166-1drg5gzp 103 15 of of IN cord-209166-1drg5gzp 103 16 applications application NNS cord-209166-1drg5gzp 103 17 in in IN cord-209166-1drg5gzp 103 18 current current JJ cord-209166-1drg5gzp 103 19 physics physics NN cord-209166-1drg5gzp 103 20 and and CC cord-209166-1drg5gzp 103 21 engineering engineering NN cord-209166-1drg5gzp 103 22 fields field NNS cord-209166-1drg5gzp 103 23 , , , cord-209166-1drg5gzp 103 24 but but CC cord-209166-1drg5gzp 103 25 it -PRON- PRP cord-209166-1drg5gzp 103 26 has have VBZ cord-209166-1drg5gzp 103 27 the the DT cord-209166-1drg5gzp 103 28 potential potential NN cord-209166-1drg5gzp 103 29 to to TO cord-209166-1drg5gzp 103 30 explain explain VB cord-209166-1drg5gzp 103 31 about about IN cord-209166-1drg5gzp 103 32 the the DT cord-209166-1drg5gzp 103 33 considerations consideration NNS cord-209166-1drg5gzp 103 34 related relate VBN cord-209166-1drg5gzp 103 35 to to IN cord-209166-1drg5gzp 103 36 outer outer JJ cord-209166-1drg5gzp 103 37 space space NN cord-209166-1drg5gzp 103 38 machineries machinery NNS cord-209166-1drg5gzp 103 39 with with IN cord-209166-1drg5gzp 103 40 special special JJ cord-209166-1drg5gzp 103 41 focus focus NN cord-209166-1drg5gzp 103 42 on on IN cord-209166-1drg5gzp 103 43 lubrication lubrication NN cord-209166-1drg5gzp 103 44 systems system NNS cord-209166-1drg5gzp 103 45 . . . cord-209166-1drg5gzp 104 1 Curvature curvature NN cord-209166-1drg5gzp 104 2 of of IN cord-209166-1drg5gzp 104 3 the the DT cord-209166-1drg5gzp 104 4 Ellipsoid Ellipsoid NNP cord-209166-1drg5gzp 104 5 with with IN cord-209166-1drg5gzp 104 6 Cartesian Cartesian NNP cord-209166-1drg5gzp 104 7 Coordinates Coordinates NNP cord-209166-1drg5gzp 104 8 RT RT NNP cord-209166-1drg5gzp 104 9 , , , cord-209166-1drg5gzp 104 10 SM SM NNP cord-209166-1drg5gzp 104 11 and and CC cord-209166-1drg5gzp 104 12 KP KP NNP cord-209166-1drg5gzp 104 13 would would MD cord-209166-1drg5gzp 104 14 like like VB cord-209166-1drg5gzp 104 15 to to TO cord-209166-1drg5gzp 104 16 thank thank VB cord-209166-1drg5gzp 104 17 School School NNP cord-209166-1drg5gzp 104 18 of of IN cord-209166-1drg5gzp 104 19 Physical Physical NNP cord-209166-1drg5gzp 104 20 Sciences Sciences NNPS cord-209166-1drg5gzp 104 21 ( ( -LRB- cord-209166-1drg5gzp 104 22 SPS SPS NNP cord-209166-1drg5gzp 104 23 ) ) -RRB- cord-209166-1drg5gzp 104 24 and and CC cord-209166-1drg5gzp 104 25 Academic Academic NNP cord-209166-1drg5gzp 104 26 Section Section NNP cord-209166-1drg5gzp 104 27 of of IN cord-209166-1drg5gzp 104 28 NISER NISER NNP cord-209166-1drg5gzp 104 29 , , , cord-209166-1drg5gzp 104 30 Bhubaneswar Bhubaneswar NNP cord-209166-1drg5gzp 104 31 where where WRB cord-209166-1drg5gzp 104 32 they -PRON- PRP cord-209166-1drg5gzp 104 33 got get VBD cord-209166-1drg5gzp 104 34 the the DT cord-209166-1drg5gzp 104 35 opportunity opportunity NN cord-209166-1drg5gzp 104 36 to to TO cord-209166-1drg5gzp 104 37 interact interact VB cord-209166-1drg5gzp 104 38 with with IN cord-209166-1drg5gzp 104 39 wonderful wonderful JJ cord-209166-1drg5gzp 104 40 members member NNS cord-209166-1drg5gzp 104 41 and and CC cord-209166-1drg5gzp 104 42 professors professor NNS cord-209166-1drg5gzp 104 43 who who WP cord-209166-1drg5gzp 104 44 helped help VBD cord-209166-1drg5gzp 104 45 them -PRON- PRP cord-209166-1drg5gzp 104 46 a a DT cord-209166-1drg5gzp 104 47 lot lot NN cord-209166-1drg5gzp 104 48 with with IN cord-209166-1drg5gzp 104 49 the the DT cord-209166-1drg5gzp 104 50 basics basic NNS cord-209166-1drg5gzp 104 51 of of IN cord-209166-1drg5gzp 104 52 Fluid Fluid NNP cord-209166-1drg5gzp 104 53 Dynamics Dynamics NNPS cord-209166-1drg5gzp 104 54 . . . cord-209166-1drg5gzp 105 1 They -PRON- PRP cord-209166-1drg5gzp 105 2 also also RB cord-209166-1drg5gzp 105 3 acknowledge acknowledge VBP cord-209166-1drg5gzp 105 4 the the DT cord-209166-1drg5gzp 105 5 support support NN cord-209166-1drg5gzp 105 6 of of IN cord-209166-1drg5gzp 105 7 their -PRON- PRP$ cord-209166-1drg5gzp 105 8 parents parent NNS cord-209166-1drg5gzp 105 9 who who WP cord-209166-1drg5gzp 105 10 constantly constantly RB cord-209166-1drg5gzp 105 11 kept keep VBD cord-209166-1drg5gzp 105 12 them -PRON- PRP cord-209166-1drg5gzp 105 13 motivated motivated JJ cord-209166-1drg5gzp 105 14 throughout throughout IN cord-209166-1drg5gzp 105 15 the the DT cord-209166-1drg5gzp 105 16 project project NN cord-209166-1drg5gzp 105 17 during during IN cord-209166-1drg5gzp 105 18 the the DT cord-209166-1drg5gzp 105 19 COVID-19 COVID-19 NNP cord-209166-1drg5gzp 105 20 Pandemic Pandemic NNP cord-209166-1drg5gzp 105 21 and and CC cord-209166-1drg5gzp 105 22 did do VBD cord-209166-1drg5gzp 105 23 n't not RB cord-209166-1drg5gzp 105 24 let let VB cord-209166-1drg5gzp 105 25 their -PRON- PRP$ cord-209166-1drg5gzp 105 26 morale morale NN cord-209166-1drg5gzp 105 27 down down RP cord-209166-1drg5gzp 105 28 . . .