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A cylindrical dinner plate is spinning out in space. It has mass $$m_p =$$ $$kg$$, radius $$r =$$ $$m$$ and it rotates clockwise (as seen from above) times every second. A (non-rotating) cylindrical cake is shot at it and the cake sticks to the surface of the plate. The cake has a mass $$m =$$ $$kg$$ and radius $$r =$$ $$m$$. In the end, both the cake and the plate rotate together.

## Part 1#

Calculate the initial angular velocity of the plate.

Please enter in a numeric value in .

## Part 2#

Calculate the moment of interia of the plate.

Please enter in a numeric value in .

## Part 3#

Calculate the initial angular momentum of the system.

Please enter in a numeric value in .

## Part 4#

Calculate the final angular velocity of the system.

Please enter in a numeric value in .

## Part 5#

How much energy is dissipated in the collision?