AP Physics C – A Free Response Practice Question on Rotation

Essential points and some practice questions on rotational motion have been discussed on this site earlier. You can access all posts related to rotational motion on this site by clicking on the label ‘rotation’ below this post.

Today we will discuss a free response question (for practice) in this section. This

question is meant for AP Physics C aspirants:

A solid cylinder of mass M and radius R has a light inextensible string wound round it. The free end of the string is tied to a rigid support (Fig.) and the cylinder is released from its state of rest.

(a) Determine the acceleration ‘a’ of the cylinder as it moves down, unwinding the string.

The cylinder itself is now suspended from the support so that it is free to rotate about its axle. The friction at the axle of the cylinder is negligible. A mass M₁ is now attached to the free end of the string wound round the cylinder as shown in the adjoining figure and the system is released from rest at time t = 0. Now answer the following questions (b), (c) and (d):

(b) Determine the acceleration a₁ of the mass M₁ in terms of the given parameters.

(c) In terms of the given parameters obtain the angular acceleration of the cylinder when the mass M₁ moves down, unwinding the string.

(d) Determine the kinetic energy of the cylinder at time t.

Try to answer this question which carries 15 points. You have 15 minutes at your disposal. I’ll be back with a model answer for you shortly.

Meanwhile find some useful multiple choice questions with solution in this section at physicsplus.