A turntable of radius 25 cm and rotational inertia 00154 kgm

A turntable of radius 25 cm and rotational inertia 0.0154 kg·m2 is spinning freely at 20.0 rpm about its central axis, with a 17.5 g mouse on its outer edge. The mouse walks from the edge to the center.

(a) Find the new rotation speed. (rpm)

(b) Find the work done by the mouse. (mJ)

I think I got part A correct, but I cannot get part B. Thanks!

Solution

A. conservation of angular momentum

Li = Lf

Ii*wi = If*wf

wf = (Ii/If)*wi

wf= [(0.0154 + 0.0175*0.25^2)/0.0154]*20 = 21.42 rpm

W = dKE

W = 0.5*If*wf^2 - 0.5*Ii*wi^2

wi = 20 rpm = 2.094 rad/sec

wf = 21.42 rpm = 2.243 rad/sec

W = 0.5*0.0154*2.243^2 - 0.5*(0.0154 + 0.0175*0.25^2)*2.094^2

W = 2.57 mJ