# Turntable, block, and rotation angular velocity

• abeltyukov
In summary, the problem involves a 200g turntable rotating at 60 rpm with a 20g block at the center. A compressed spring causes the block to move radially outward along a frictionless groove on the turntable's surface. The question asks for the turntable's angular velocity when the block reaches the outer edge. To solve this, conservation of angular momentum should be used, making sure to account for the moment of inertia. The solution involves equating the rotational kinetic energy of the turntable to that of the turntable and block system.
abeltyukov

## Homework Statement

A 200g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a frictionless groove in the surface of the turntable. What is the turntable's rotation angular velocity when the block reaches the outer edge?

1/2Iw^2
I = 1/2MR^2

## The Attempt at a Solution

I did:
1/2Iw^2 = 1/2Iw^2
1/2(1/2(0.200)(0.20)^2)(2pi)^2 = 1/2(1/2(0.200)+0.020)(wf)

Does that seem right?

Thanks!

You have to use conservation of angular momentum. I'm not sure what you did in the equation 1/2(1/2(0.200)(0.20)^2)(2pi)^2 = 1/2(1/2(0.200)+0.020)(wf). The angular momentum of the turntable and the block in the center must equal the angular momentum of the turtable with the block on the edge. Watch out for the moment of inertia.

I did rotational kinetic energy of the turntable = rotational kinetic energy of the turntable and block. So KE = 1/2Iw^2. Can I do that?

Thanks!

## 1. What is a turntable?

A turntable is a rotating platform used for playing records, commonly known as a record player. It usually consists of a circular platter, a motor, and a tonearm with a stylus for playing the record.

## 2. What is a block in relation to turntable and rotation angular velocity?

In the context of turntable and rotation angular velocity, a block refers to a material or object that is placed on the turntable and used to measure its rotational speed or angular velocity. This is often done by measuring the time it takes for the block to complete one full rotation on the turntable.

## 3. How is angular velocity calculated for a turntable?

Angular velocity is calculated by dividing the angle of rotation (in radians) by the time it takes to complete that rotation. This can be represented as ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angle, and Δt is the change in time.

## 4. How does the mass of the block affect the rotation angular velocity of a turntable?

The mass of the block does not directly affect the rotation angular velocity of a turntable. However, it can affect the amount of force required to rotate the turntable, which can ultimately impact the turntable's angular velocity.

## 5. What factors can affect the rotation angular velocity of a turntable?

The rotation angular velocity of a turntable can be affected by various factors such as the motor speed, the size and weight of the turntable, the friction between the turntable and the surface it sits on, and any additional load or weight placed on the turntable. The type and condition of the stylus used can also impact the rotation angular velocity.

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