Answer
See answers.
Work Step by Step
a. There is no net external torque on the wheel-people system, so its net angular momentum is conserved.
We assume the people have no initial angular momentum. The final angular velocity is the same for everything.
$$L_{i}=L_{f}$$
$$I_i \omega_i = I_f \omega_f$$
$$\omega_f =\omega_i \frac{I_i }{I_f} $$
Find initial and final moments of inertia.
$$I_i=1360 kg \cdot m^2$$
$$I_f=1360 kg \cdot m^2 + 4M_{person}R_{wheel}^2=2506.6 kg \cdot m^2$$
The initial frequency is given, so evaluate to find the final frequency.
$$\omega_f =(0.80rad/s) \frac{I_i }{I_f}=0.43 rad/s $$
b. The people jump off the merry-go-round radially. They exert no torque on the merry-go-round and do not change the angular momentum of the merry-go-round, which would therefore keep its initial angular velocity of 0.80 rad/s.
