Elastic collision between rod and ball

[tilaib]

Homework Statement

A rod of mass M is lying on a flat frictionless surface. A small ball of mass m and
velocity v collides with the rod in the center at the rod at right angle to the rod.
The collision is elastic.

Homework Equations

a) Where is the axis of rotation for the rod after the collision?
b) What is the angular velocity around the axis of rotation after this collision?
c) What is the velocity of the center of mass of the rod after the collision?

The Attempt at a Solution

As far as I can see, there should be no rotation. But how do I show this?

 

[barryj]

You might assume that there is a rotation, then in the process of calculating what the rotation would be, you might find there is none. Many proofs are done this way in that it might be hard to prove something is always true but easy to fine one example of a falsehood to disprove your original hypothesis.

 

[haruspex]

tilaib, I agree with barryj, but it does seem strange that the question asks about rotation twice. Are you quite certain you are reading the statement of the set-up correctly?