Turntable Problem: Homework Solution

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The discussion revolves around a physics problem involving a turntable with a girl moving from the center to the edge. The key questions are determining the angular velocity of the turntable when the girl reaches the edge and calculating the minimum coefficient of static friction required to prevent her from slipping. Participants emphasize the conservation of angular momentum as the relevant principle, noting that the initial and final states can be expressed in terms of moment of inertia and angular velocity. There is some confusion regarding the relationship between velocity and other quantities, particularly due to missed classes. The conversation highlights the importance of understanding conservation laws in solving rotational dynamics problems.
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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).
 
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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?
 

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