Question

A 21.1-N force is applied to a cord wrapped around a pulley of mass M = 4.49-kg and radius R = 25.0-cm The pulley accelerates uniformly from rest to an angular speed of 25.5 rad/s in 2.31-s. If there is a frictional torque \tau = 2.80-mN at the axle,

(a) determine the moment of inertia of the pulley,

(b) determine the rough estimate of the moment of inertia.

(The pulley rotates about its center)

What is the difference be (a) and (b)?

Answer 1

The difference between (a) and (b) is the deviation caused by the actual pulley not being a perfect solid disk. In (a), we took into account the additional frictional torque and calculated the more accurate moment of inertia. In (b), we made a rough estimate assuming the pulley to be a solid disk, which disregards factors such as the mass distribution and the presence of the axle. The difference between the two values is the deviation caused by these factors.