Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.05 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.07 m from the axis of rotation and the student rotates with an angular speed of 0.740 rad's. The moment of inertia of the student plus stool is 2.57 kg: m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.307 m from the rotation axis (Figure b). 0 (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. K before Kiter 3
please guys this is one question with 2 parts.

Answer 1

11 When the stretched his arent W Hart Proment of eventia with stol and from axen array The system deumble The demshe hasse has man w=3.08 kg et t reteten at 2.2 (com Se moment enterta of each chumble Isa mga [ 85x40th] regra I rotating with angulen velocete w-0-740 sed is . Angular unorcenter of the person e Iwi - There are are two dimbles dumbler. So the total angeler momenten for both of them 2001y. 2(In ws) : Net inital angular momentin L. Is wit 2 (I, Wi) Wita, Low(1,+212) Li --0-74(2 2.57 + 2x3.054 1.072 Li - 7.0698 kgents? o es Wer he pull the dumbles en wand: In this time his moment of morto in so erwir angular momentem. If we name,

Ping 2 Now sind angle anguler sprede the new distance of dumbles from So, ets moment 23.09 x 60-307) 2 kqw? es - 807m 0-307m 2 of eventa es Iza m LA 1 - The Their to let angulen momentan) = 24 (Iz ws) there are baro dumble So to te send angulen womentur, Ls = I wst 2 Iz wf wf (I, + 25. Nad Now, from the conservation of angeles womenten, enital angular momentur = send arguilar womentrer. : Itw 21 21 g 7-0698 wf (I, +2 I₃) 7-8698 OM - we I +213 7.0698 2.52+273.05 r(d 30 31 =99 Dots 2. 25 rad ist – Thin Abs roguard snad angules veleels.

(1) Initial kinetic energy? -: Tot enite al kinetic energy, If I be the moment of events and w be the angular velocity, then sotational kinetic e energy es defined as a = I w² - Ulring the formulas, bet a calculate the toto enstral kinetic energy. - K before a kinete energy of man with stool +2x kinete energy of dut dumble there are r. dumble ) = I, w 2 + Ig wi2 2. 2 - 2x (2.57+ 2x305x1022) wa 6-742 Ik ben I am do = 2.61 Tail por

kaster Total final kuretic energy / semilarly 1 I, wp? Iz wg2th - (T1 491,) woga Fesz. mod - (2:54 + 2x 3.05 +0.2021) 48.933 - 7.90 Touls Katto consider the semplified diagram. 0 Let un Initial Find os Imetal Finel nee the the total angeler disple.ce- moment from positon to en shown in periton 3. Stote sangeles cisto desplecement AO= 0 + Of = 20° +20° 7200 (From fog : 3) Trad 20 Y (SD Ad 0-688 rad to angular displacement e dove in 720698 nec ta 1-2 reo DO 0-698 - Angular velocity to A w=0.5817 sodas

I Page 5 The radius of rotation - height of the leg 2085 ara 0-85 mm Moment of exunertat a hasha mon y vadres of sot too Box 70 x (0-89² 56.358 kgm2 te we can consider the whole center of es rotated about the red poent on ground & Angular wonenter, La - 56.389 x 0-5817 IL 232.782 kg mis
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