# Determine the translational and rotational motion

1. Oct 6, 2009

### LBloom

1. The problem statement, all variables and given/known data

A thin rod of mass M and length L rests on a frictionless table and is struck L/4 from its CM by a clay ball of mass m moving at speed v. The ball sticks to the rod. Determine the translational and rotational motion.

2. Relevant equations
Irod=1/12*M*R^2
I=mR^2
L=Iw or L=r*m*v
L=constant

3. The attempt at a solution

I figured out the answer for the first part, but the second part has me stuck. I got:
m*v*L/4=(Irod+1/16*m*L^2)*w, where Irod=1/12*M*R^2

When i solve for w i get: [12m/(4M+3m)]*v/L
However the textbook says the answer is: [12m/(4M+7m)]*v/l

It looks like a made a mistake when calculating the moment of inertia for the clay blob, but i dont know where i made the mistake. I think it was in the beginning with Lbefore=Lafter, but i dont see it.

2. Oct 7, 2009

### ehild

The rod+ball will rotate around their new centre of mass, so you have to calculate the original angular momentum of the ball with respect to it, and also the moment of inertia of the whole system has to be calculated with respect to this new CM.

ehild