Determine the translational and rotational motion

[LBloom]

Homework Statement

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.

Homework Equations

I_rod=1/12*M*R^2
I=mR^2
L=Iw or L=r*m*v
L=constant

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 don't know where i made the mistake. I think it was in the beginning with Lbefore=Lafter, but i don't see it.

 

[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

 

[tomcue]

I would first check the equations used and verify if they are appropriate for the given scenario. The moment of inertia for a thin rod should be Irod=1/12*m*L^2, not 1/12*M*R^2. Additionally, the conservation of angular momentum equation should be Lbefore=Lafter, not L=constant. After correcting these equations, the final answer should be [12m/(4M+3m)]*v/L, which is the same as your solution. It is possible that the textbook answer is incorrect or there is a typo.