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- Homework Statement
- Perfectly inelastic collision of two moving and rotating disk

- Relevant Equations
- angular momentum, momentum

two moving and rotating, uniformly weighted disks perfectly inelastic collide. The disks are rotating in opposite directions (see the diagram) At the moment of their collision, the angles between their velocity and the line connecting their centers are 45 degrees. The velocities are therefore in right angle. We know their angular velocity, their velocities, their radii and their masses. Find the angular velocity after collision.

My thought. Let the center of the mass of the entire system be our reference. We can then ignore the linear momentum and only work on the angular momentum.

The angular momentum of wheel 1 w.r.t center of mass of the whole system is

I

similarly compute angular momentum of wheel 2 w.r.t center of mass of the whole system.

But I got stuck on computing v'

Can someone first comment if my above approach is correct, also comment how to find v'

My thought. Let the center of the mass of the entire system be our reference. We can then ignore the linear momentum and only work on the angular momentum.

The angular momentum of wheel 1 w.r.t center of mass of the whole system is

I

_{1}ω_{1}+ m_{1}v'_{1}, where v'_{1}is the vertical relative velocity with respect to the center of the mass of the system,similarly compute angular momentum of wheel 2 w.r.t center of mass of the whole system.

But I got stuck on computing v'

_{1}Can someone first comment if my above approach is correct, also comment how to find v'

_{1}?
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