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× e physics question ! Chego x ? ??C Secure l https://edugen.wileyplus.com/ed Halliday,Fundaentals of Physics, 10e ASSIGNMENT RFSOURCFS Chapter 11, Problem 052 SN A cockroach of mass m lies on the nm of a uniform disk o mass 4m that can rotate reely about its center like a merry go round init ally the cockroach and disk rotate together with an angular velocity of ?? Then the cockroach walks halfway ta the center of the disk. (a) What then is the angular velacity of the cockroach-disk system? (h) What is the ratia KK of the new kinetic energy of the system to its initinl kinelic eneyy? Slle your answer in Lesof he yiven variables Click here to enter or edit chapter D9, Prohlm chapter D9, Prohlm chapter 10, Prohlm Click if you would like to Show Work for this question Question Attempts: Unlimited SAVE FOR LATER chapter 11, Prohlem https:/fedugert.wileyplus.coumvedugerýshared assigrentestfeglist.uniid-asimi21393184N101AC O Type here to search D e 842 AM 46/2018Explanation / Answer
Moment of inertia of disk = 4 m r2/2 = 2 m r2
Moment of inertia of cockroach when at rim = mr2
Moment of inertia of cockroach when half way to center of disk = m(r/2)2 = mr2/4
Initial moment of inertial of disk + cockroach system = 2mr2 + mr2 = 3mr2
Final moment of inertial of disk + cockroach system = 2mr2 + mr2/4 = 9mr2/4
Angular momentum of the system, Iw, remains conserved, as cockroach moves to the center.
hence 3mr2wo = 9mr2w/4 ( wher w is final angular veloctiy of system)
w = 4wo/3
Kinetic energy of rotating system = Iw2/2 = L2/2I ( where L is angular momentum of system)
Since angular momentum, L remains constant
k1 I1 = K2 I2
Ko(3mr2) = K (9mr2/4)
K / Ko = 4/3
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