Answer
The angular speed is $~~8.4~rad/s$
Work Step by Step
In part (b), we found that the initial angular speed is $~\omega_i = 0.933~rad/s$
In part (c), we found that the initial rotational inertia of the system is $~I_i = 225~kg~m^2$
We can find the initial angular momentum:
$L_i = I_i~\omega_i$
$L_i = (225~kg~m^2)(0.933~rad/s)$
$L_i = 209.9~kg~m^2/s$
We can find the final rotational inertia of the system when the radius of the circle is $0.5~m$:
$I_f = m_1r^2+m_2r^2$
$I_f = (50~kg)(0.5~m)^2+(50~kg)(0.5~m)^2$
$I_f = 25~kg~m^2$
We can use conservation of angular momentum to find the new angular speed:
$L_f = L_i$
$I_f~\omega_f = 209.9~kg~m^2/s$
$\omega_f = \frac{209.9~kg~m^2/s}{I_f}$
$\omega_f = \frac{209.9~kg~m^2/s}{25~kg~m^2}$
$\omega_f = 8.4~rad/s$
The angular speed is $~~8.4~rad/s$.
