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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 [tex]\frac{v}{6R}[/tex]. I didn't realized it and thought that the kinetic energy would be conserved and I got a result of [tex]\omega=\frac{v}{\sqrt{6}R}[/tex]. As [tex]\omega=\frac{v}{\sqrt{6}R} > \frac{v}{6R}[/tex] it means the system loses kinetic energy by a factor [tex]\frac{1}{\sqrt 6}[/tex]. 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.

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# Rigid body/perfectly plastic collision question

Can you offer guidance or do you also need help?

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