Cat & Turntable: Angular Velocity Comparison?

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When a cat walks around the edge of a stationary turntable of the same mass, angular momentum must be conserved. As the cat moves, it exerts a force that causes the turntable to rotate in the opposite direction. The angular velocities of the cat and the turntable are inversely related, meaning that as the cat increases its speed, the turntable rotates slower to conserve momentum. The mathematical relationship can be derived by considering the moment of inertia and angular velocity of both the cat and the turntable. Therefore, the cat must move to ensure that the total angular momentum remains constant.
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If there's a cat and a turntable both of same mass each... and the cat starts walking around the edge of the turntable which is initially at rest, how would the angular velocity of the two objects compare? Would the cat move at all since it has the same mass as the turntable and momentum has to be conserved??
 
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Yes, the cat would have to move to conserve angular momentum. Can you show why? Assume the turntable is a disk of radius R and work it out.
 

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