Answer
$0.1 rad/s$ , $0.4 rad/s$
Work Step by Step
The initial and final angular velocities can be calculated as follows:
$a=\frac{F}{m}$
$\implies a=\frac{150}{100}=1.5m/s^2$
Similarly, $\Delta \theta=\frac{125}{50}=2.5 rad$
Now $\omega_i=\frac{\Delta \theta}{t}-\frac{at}{2r}$
We plug in the known values to obtain:
$\omega_i=\frac{2.5}{10}-\frac{1.5\times 10}{2\times 50}$
This simplifies to:
$\omega_i=0.1 rad/s$
and $\omega_f=\omega_i+\frac{at}{r}$
We plug in the known values to obtain:
$\omega_f=0.1+\frac{1.5\times 10}{50}$
This simplifies to:
$\omega_f=0.4 rad/s$
