Two objects with mass of m are connected with a rod with length 2l and with no mass. The center of the rod is pinned so that it can spin. Object with mass M comes with speed v and sticks to m. There is no friction.
1) What is the angular speed w after collision?
2) FInd the value and the direction of Impulse that was sent through the rod during collision
3) Right after collision, find the value and the direction of the force acting on the rod by the center of the rod
As an alternate version of this question, suppose that the collision was perfect elastic collision and that the velocity after collision was v1 for M and v2 for m (the direction of the velocity didn't change). M>2m
4) Find the value of v1
5) Find the value of impulse sent through the rod
Conservation of momentum and angular momentum
The Attempt at a Solution
1) I don't know whether linear and angular momentum are exchangeable. So I used only linear momentum. Mv= (M+2m)v1 and solved for v1.
2) The collision happens at the left side of the rod but the right side of the rod moves as well, and it does at velocity v1. The momentum for the object on the right side changes from 0 to mv1 so the impulse should be mv1 to direction -y
3) I didn't really get this question. But I though that perhaps it has got to do with the center of the rod not being the same as the center of mass.
4) Mv=Mv1+2mv2 and (v2-v1)/(v-0)=1. So v1=(M-2m)v/(M+2m)
5) Thinking the same way as I did in 2) I answered mv2
I tried to answer all the questions but I'm not sure if they are correct. If you could check these I would be thankful