Question

A turntable with a moment of inertia of 4.9 kg · m2 rotates freely with an angular speed of 33 1/3 rpm. Riding on the rim of the turntable, 12 cm from the center, is a cute, 3.2-g mouse. Calculate the angular speed of the turntable when the mouse reaches the center.

Answer 1

Use the conservation of angular momentum.\[\Large L_i = L_f \longrightarrow I_i \omega_i = I_f \omega_f \longrightarrow \omega_f = \omega_i \frac{I_i}{I_f}\]Here, the moment of inertia is changing.

Answer 2

Adding to @yakeyglee's answer:
Moment of inertia is given by I=mr^2
here, when mouse reaches center of table moment of inertia decreases by
(3.2*10^-3)*(12*10^-2)^2

So final moment of inertia \[I_f=I_i-0.00004608\]Now you can do further calculation by yourself.