AP Physics C Free Response Practice Question Involving Angular Momentum

Do not worry about your problems with mathematics; I assure you mine are far greater.

– Albert Einstein

Today I give below a free response practice question involving the concepts of moment of inertia, angular momentum, elastic collision and inelastic collision for the benefit of AP Physics C aspirants:

An object of mass m collides elastically with the lower end B of a thin uniform rod AB of mass 3m and length L suspended vertically using a frictionless hinge at its upper end A (Fig.) so that it can rotate in a vertical plane. The only external force present is that of earth’s gravity. Just before collision the object was moving horizontally with speed v. Now answer the following questions:

(a) Given that the moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its middle and perpendicular to its length is ML²/12, determine the moment of inertia of the rod AB about the hinge.

(b) Calculate the horizontal speed of the object of mass m after the collision.

(c) Suppose the colliding object were of the same mass (3m) as that of the rod. Calculate the distance d from the hinge at which the colliding object (moving with the horizontal speed v) should hit the rod so that its kinetic energy is fully transferred to the rod.

(d) If the collision at the position obtained in part (c) is such that the colliding object gets attached to the rod, calculate (in terms of the given parameters) the angular velocity with which the rod starts moving after the collision

The above question carries 15 points and you have 15 minutes at your disposal. Try to answer this question. I’ll be back soon with a model answer for your benefit.

Meanwhile find some useful multiple choice questions (with solution) in this section here.

You can find other posts involving rotation on this site (including equations to be remembered) by clicking on the label ‘rotation’ below this post.