Answer
See answers.
Work Step by Step
a. First find the angular acceleration.
$$\alpha = \frac{\Delta \omega}{\Delta t}=\frac{v/r}{t}=\frac{(8.5m/s)/(0.31m)}{0.38s}\approx 72rad/s^2$$
b. Apply Newton’s second law. The torque is the moment of inertia multiplied by the angular acceleration.
$$Frsin \theta=I \alpha$$
$$F=\frac{I \alpha}{r sin \theta}=\frac{m_{ball}(0.31m)^2+\frac{1}{3}m_{arm}(0.31m)^2}{(0.025m)sin 90}\alpha$$
$$F=619.5N\approx 620N$$