When throwing a ball, a pitcher exerts a torque of 150 N m for 0.15 seconds onto their arm before letting go of the ball. With an arm length of 0.9 m with inertia 0.6 kg m2, what is the speed of the ball just after it is released?
Torque = (moment of inertia)*(angular acceleration)
alpha = angular acceleration
= 150 N m/0.6kg/m^2
= 250 rad/s^2
w = angular velocity at release =
(angular acceleratio)*0.15 s
= 37.5 rad/s
Ball release velocity
V = w*R = 33.8 m/s = 111 ft/s
= 75.5 mph
The mass of the ball makes a significant contribution (of about 5%) to the moment of inertia of the arm, and should be included in the calculation.