Question

A disk having moment of inertia $$100kg\cdot m^2$$ is free to rotate without friction, starting from rest, about a fixed axis through its center. A tangential force whose magnitude can range from \(F = 0\) to \(F = 50.0\) N can be applied at any distance ranging from \(R = 0\) to \(R = 3.00\) m from the axis of rotation. Find a pair of values of \(F\) and \(R\) that cause the disk to complete 2.00 rev in 10.0 s. Choose the pair with the greatest force.

Answer 1

F R = I alpha
alpha = change in angular velocity omega/ time
if angular acceleration alpha is constant ( constant torque)
omega = alpha t
angle = (1/2) alpha t^2
so
2 pi * 2 = (1/2) alpha t^2
alpha t^2 = 8 pi = 25.1 radians
t = 10 seconds
so
alpha = 25.1/100 = 0.251 radians/s^2
therefore F R = 100 * 0.251 = 25.1 Newton meters
max F = 50
so R = 25.1 / 50 or about 1/2 meter