Angular Momentum Problem of turntable

[viper930]

This seems pretty basic but I am drawing a blank. Thanks in advance.

"A cat is sitting on the rim of a wooden turntable that is free to turn about a vertical axis. The turntable's mass is 3 times the cat's mass and is initially at rest. The cat then starts walking around the rim at a speed of 0.6m/s relative to the ground. How fast does the turntable's rim move relative to the ground?"

 

[Chi Meson]

conservation of angular momentum. Just like linear momentum, when two things push apart, mv of one object equals -mv of the other, in angular momentum, the Iw of one equals the -Iw of the other.

 

[kyle8921]

I would approach this problem by first considering the concept of angular momentum. Angular momentum is a measure of an object's rotational motion and is defined as the product of its moment of inertia and angular velocity. In this case, the turntable and the cat both have angular momentum due to their rotational motion.

Since the turntable is initially at rest, its initial angular momentum is zero. However, as the cat starts walking around the rim, it adds angular momentum to the system. According to the law of conservation of angular momentum, the total angular momentum of the system must remain constant.

Therefore, as the cat's angular momentum increases, the turntable's angular momentum must also increase in the opposite direction in order to maintain the balance. This means that the turntable's rim must start moving in the direction opposite to the cat's motion.

To determine the speed of the turntable's rim relative to the ground, we can use the equation for angular momentum: L=Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

We know that the cat's mass is much smaller than the turntable's mass, so we can assume that the moment of inertia of the cat is negligible compared to the turntable's moment of inertia. Therefore, we can simplify the equation to L=Iω = (3m)(0.6m/s) = 1.8m/s.

This means that the turntable's rim is moving at a speed of 1.8m/s in the opposite direction to the cat's motion. In other words, the turntable's rim is moving relative to the ground at a speed of 1.8m/s in the direction opposite to the cat's motion.