Question

A disc-shaped merry-go-round has a mass of 100 kg and a radius of 1.60 m and is initially spinning at 20.0 rpm, with a 33-kg child sitting at its center. The child then walks out to the edge of the disc. (a) Find the initial and final moments of inertia of the system (disc + child), treating the child as a point particle. (b) State why the system’s angular momentum is conserved. (You can assume that the axis of the disc is frictionless.) (c) Find the initial and final kinetic energies of the system. (d) State the physical reason for the change in kinetic energy. (I.e., what force does the work that causes the kinetic energy to change?)

Answer 1

Initial condition Fenal condtion mje M m IMR w20pM Ii= Lis Iiwis angular mamantum +MR2 Cm-33rg) Ca I:= MR IXIoD (.60= 128 Kam2 fIMRT mR2-128 + adx 1.602 = 204.8 ka m2 b) Angular momentum is Conserewed because No entermal Torque t's apPied on system Net Tnite'al kinetic Energy Cki) - Iwi -2 128 X 280.45J binal kinet'e Energy Iiwi= Ie op) 28 X 20 - 0.130 pd/s 1.25 pm 204.8 TX204.8 x 0.130 2 1.75 J (4 he meaon or Chemge in kinetic Energy is the musulor bare or boy did the ww0rk .