Conservation of Angular Momentum of Turntable Problem

AI Thread Summary
The discussion revolves around a physics problem involving a turntable and a ball, focusing on the conservation of angular momentum. Participants clarify that while the ball does not have angular velocity, it possesses linear momentum that contributes to the system's overall angular momentum when caught by the turntable. The moment of inertia of the ball, treated as a point mass at a distance from the axis, is a key consideration in calculating the new angular velocity after the ball is caught. The initial calculations presented yield an incorrect angular velocity, prompting further exploration of the conservation principles involved. Understanding the relationship between linear and angular momentum is essential for solving this problem accurately.
joshualan
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Homework Statement


A turntable with moment of inertia of 2.0kg*m^2 has a radius of 0.80m and an angular velocity of 1.5 rad/s. A ball is thrown horizontally of 0.4kg at 3.0 m/s and is caught by the turntable by a small and very light cup-shaped mechanism at the turntable's edge. What is the new angular velocity after the ball is caught?


Homework Equations


Angular momentum = Moment of Inertia * Angular Velocity
Moment of Inertia of a Disk = (1/2)MR^2
Tangential Velocity = Angular Velocity * Radius

The Attempt at a Solution


Well, I didn't really think the ball had angular velocity since it wasn't rotating so I found the tangential velocity of the turntable and used the moment of inertia to find the mass of the turntable. I then used the Law of Conservation of Momentum to find the tangential velocity of the turntable with the added mass of the ball. This is what I got:

Mass of Turntable * Tangential Velocity + Mass of Ball * Velocity of Ball = (Mass of Turntable + Mass of Ball) * New Velocity

I then solved for the new velocity which I then used to find the new angular velocity. The answer I got (1.6 rad/s) were not one of the choices in the question so I'm assuming I'm wrong.

How can a non-rotating ball have an angular velocity? I'm sure that this is the key somehow.
 
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The turntable is attached to the axis. The axis exerts force. In such case the linear momentum does not conserve. Work with the angular momentum.
Does the ball have angular momentum with respect to the axis before it is caught at the rim of the turntable? It is small, and does not rotate, but it has a linear velocity and its distance from the axis of rotation is R at that instant.

ehild
 
ehild said:
The turntable is attached to the axis. The axis exerts force. In such case the linear momentum does not conserve. Work with the angular momentum.
Does the ball have angular momentum with respect to the axis before it is caught at the rim of the turntable? It is small, and does not rotate, but it has a linear velocity and its distance from the axis of rotation is R at that instant.

ehild

The radius of the ball itself is not given though so how can I calculate its moment of inertia?
 
It has moment of inertia with respect to the axis. What is the moment of inertia of a point mass m at distance r from the axis?

ehild
 
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