Cat & Turntable: Angular Velocity Comparison?

[physgirl]

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??

 

[OlderDan]

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.

 

[kyle8921]

The angular velocity of the two objects would not be directly comparable as they have different rotational properties. The turntable is a rigid object with a fixed axis of rotation, while the cat is a living organism capable of changing its direction and speed. However, the cat's movement around the edge of the turntable would cause a change in the overall angular momentum of the system. This is because the cat's movement is also a form of angular motion, and according to the law of conservation of angular momentum, any change in one part of a system must be balanced by an equal and opposite change in another part. Therefore, the turntable would start to rotate in the opposite direction to the cat's movement in order to conserve the total angular momentum of the system. The cat's movement would also be affected by the turntable's rotation, as it would experience a centripetal force pulling it towards the center of the turntable. In conclusion, while the angular velocities of the two objects may not be directly comparable, they are intrinsically linked through the conservation of angular momentum.