# Rigid body/perfectly plastic collision question

1. Dec 4, 2008

### fluidistic

1. The problem statement, all variables and given/known data
Today a friend of mine came to my apartment and we discussed a problem. I realized something that surprises me A LOT.
Consider the following situation. There are 2 disks of radius R and mass M on a frictionless table. One doesn't move while the other suffers a translation with speed v and will hit the quiet disk such that its lowest point will touch the upper point of the other disk. When it hits it, the two disks remain attached forming a new rigid body.
Calculate the angular velocity of the rigid body.
I think one gets the answer using the conservation of angular momentum or something like that. The result is $$\frac{v}{6R}$$. I didn't realized it and thought that the kinetic energy would be conserved and I got a result of $$\omega=\frac{v}{\sqrt{6}R}$$. As $$\omega=\frac{v}{\sqrt{6}R} > \frac{v}{6R}$$ it means the system loses kinetic energy by a factor $$\frac{1}{\sqrt 6}$$. Why such a number? Is that true with any plastic collision?
And another question : How does this energy converts itself into heat? There's no friction nor elastic deformation due to compression since we're talking about rigid bodies. I don't see any way to convert the energy. Hence I'm missing something... can you help me answering some (or all) these questions ?
Thanks.