Velocity of COM after collision

[Mooy]

Homework Statement

Show that the velocity of the centre mass of the body is zero immediately after impact if the following equation holds.
b^2=(e•l^2)/12
Note: The head is released from rest and the only force acting on the head during impact is at point A

Relevant Equations

KE=0.5mv^2
GPE=mgh
V=rω
I=(ml^2)/12

I calculated that the velocity of the head prior to the collision is sqrt(2gh), as all of the gravitational potential energy is converted to kinetic energy.

And I believe the velocity at point A after the collision is given by the formula vf=e•sqrt(2gh), with e representing the coefficient of restitution. As the ground does not change in velocity during the collision.

I believe that the head is meant to be treated as a rod with a moment of inertia of (ml^2)/12.

I’m unsure how to go about getting the centre of mass to have zero velocity, any help would be greatly appreciated

 

[TSny]

Have you covered the "impulse-momentum theorem" and the corresponding "angular impulse-angular momentum theorem"?

Recall that angular momentum is always calculated relative to some point ("origin"). What would be a good choice for the origin in this problem?

 

[Mooy]

Have you covered the "impulse-momentum theorem" and the corresponding "angular impulse-angular momentum theorem"?

Recall that angular momentum is always calculated relative to some point ("origin"). What would be a good choice for the origin in this problem?

Thanks heaps think I get it now.

Would it be to conserve angular momentum about A, and the COM has an initial angular momentum of sqrt(2gh)mb prior to the collision.
I forgot that an object without angular velocity still has angular momentum

 

[haruspex]

Thanks heaps think I get it now.

Would it be to conserve angular momentum about A, and the COM has an initial angular momentum of sqrt(2gh)mb prior to the collision.
I forgot that an object without angular velocity still has angular momentum

That will give the desired answer, when combined with your two beliefs in post #1.