# Turntable Problem: Homework Solution

• teeheehee
In summary: Angular momentum?In summary, a girl of mass 30 kg standing at the exact center of a large turntable with a radius of 6 m and a moment of inertia of 500 kg m^2, is rotating with an angular velocity of 1 radian/s. When she moves slowly outward to the edge of the turntable, the angular velocity of the turntable changes. To remain fixed at the edge without slipping, the minimum coefficient of static friction between the girl and the turntable must be calculated. The conserved quantities in this system are angular momentum and kinetic energy, and they can be calculated using the given information. The student is unsure of how to relate velocity to these quantities.
teeheehee

## Homework Statement

A large turntable of radius 6 m and moment of inertia I = 500 kg m^2
about its center is rotating with an angular velocity of 1 radian/s. A girl of mass 30 kg standing at the exact center moves slowly outward to the edge of the turntable.

a) What is the angular velocity of the turntable when she reaches the edge?
b) Now that she is at the edge what is the minimum coefficient of static friction between the girl and the turntable such that she remains fixed at the edge without slipping?

## Homework Equations

L = Iω, mRω^2= u mg, K =1/2 Iω^2
Not sure what else?

## The Attempt at a Solution

I played around with the moment of inertia equation for a disc, but didn't get very far. I'm not sure how I can relate velocity to everything (I missed all of these classes since I was really sick).

teeheehee said:

## Homework Statement

A large turntable of radius 6 m and moment of inertia I = 500 kg m^2
about its center is rotating with an angular velocity of 1 radian/s. A girl of mass 30 kg standing at the exact center moves slowly outward to the edge of the turntable.

a) What is the angular velocity of the turntable when she reaches the edge?
b) Now that she is at the edge what is the minimum coefficient of static friction between the girl and the turntable such that she remains fixed at the edge without slipping?

## Homework Equations

L = Iω, mRω^2= u mg, K =1/2 Iω^2
Not sure what else?

## The Attempt at a Solution

I played around with the moment of inertia equation for a disc, but didn't get very far. I'm not sure how I can relate velocity to everything (I missed all of these classes since I was really sick).

What quantity is conserved in the system? Can you write expressions for it for the initial state and final state?

gneill said:
What quantity is conserved in the system? Can you write expressions for it for the initial state and final state?

Momentum? Inertia? Honestly I have no clue of where to start here.

You're given the moment of inertia for the disk. You're given the initial rotation rate of the disk. What conserved quantity can you calculate from that?

gneill said:
You're given the moment of inertia for the disk. You're given the initial rotation rate of the disk. What conserved quantity can you calculate from that?

Kinetic energy?

Kinetic energy is not always conserved, particularly when something in the system is moving about under its own power.

What other conserved quantity do you know?

## 1. What is the Turntable Problem?

The Turntable Problem is a popular physics problem that involves a rotating turntable and a person standing on it. The question typically asks for the minimum speed at which the turntable must rotate in order for the person to not slip off.

## 2. How do you solve the Turntable Problem?

To solve the Turntable Problem, you need to use the concept of centripetal force and the equation F=mv^2/r. The centripetal force is equal to the weight of the person, and by setting this equal to the equation, you can solve for the minimum speed.

## 3. What are the key assumptions made in solving the Turntable Problem?

The key assumptions in solving the Turntable Problem are that the person on the turntable is not moving relative to the turntable, the turntable is a perfect circle, and there is no friction between the person's feet and the turntable.

## 4. Can the Turntable Problem be solved using different methods?

Yes, the Turntable Problem can be solved using different methods such as using the concept of torque and angular momentum. However, the most commonly used method is using the concept of centripetal force.

## 5. What real-life applications does the Turntable Problem have?

The Turntable Problem has many real-life applications, such as determining the safe speed for a car to take a turn without skidding, calculating the speed needed for a rollercoaster to stay on its track, and designing centrifuges for separating substances based on their densities.

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