Angular Velocity of a turntable-man system

In summary, a turntable with a moment of inertia of 1600kgm^2 rotates about a fixed axis, completing one revolution in 10 seconds. James Bond, with a mass of 120kg, begins to run along a radius of the turntable, treated as a point object. The initial angular velocity and momentum are calculated, and then the angular velocity of the turntable-man system when the man is 2m from the center is determined. This is done by adding the man's inertia (calculated using mr^2) to the turntable's inertia. Using the conservation of angular momentum, the final angular velocity is found to be constant since there is no external torque acting on the turntable.
  • #1
Kizaru
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Homework Statement


A turntable rotates about a fixed vertical axis, making one revolution in 10s. The moment of inertia of the turntable about the axis is 1600kgm^2. A man, James Bond, of mass 120kg, is at the center of the turntable and begins to run out along a radius of the device. Treat the man as a point object.


Homework Equations


L = Iw


The Attempt at a Solution


There are three parts. The first part asks for the initial angular velocity, which is simply converting 1rev/10s into rad/s. The second part asks for the initial angular momentum, which would be L = Iw?

The third part is asking for the angular velocity of the turntable-man system when the man is 2m from the center of the turntable. It also says at this point the man is at rest with respect to the turntable.

Now I run into my problems. I'm not too sure about how to calculate this, but one method I'm thinking of is recalculating the inertia to be 1600kgm^2 + mr^2 where m and r are referring to the man (so 120kg and 2m respectively). This would give an inertia of 1840kgm^2.

I thought about using L = r (cross) p, but solving for the linear momentum would mean finding Vtan = wr? How would I find w in this case?
 
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  • #2
Since there is no external torque acting on the tern table, angular momentum remains constant.
 
  • #3
I was considering that approach but wasn't sure. Thanks. However, my approach to the new inertia would be correct, I assume?
 
  • #4
Yes.
 

1. What is the definition of angular velocity?

Angular velocity is a measure of how quickly an object is rotating around a fixed point or axis. It is typically measured in radians per second.

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angle by the change in time. This can be represented by the equation ω = Δθ/Δt, where ω is angular velocity, Δθ is the change in angle, and Δt is the change in time.

3. What is the relationship between linear and angular velocity?

The relationship between linear and angular velocity is given by the equation v = rω, where v is linear velocity, r is the radius or distance from the axis of rotation, and ω is angular velocity. This means that as the radius increases, the linear velocity also increases for a given angular velocity.

4. How does the angular velocity of a turntable-man system affect the man standing on the turntable?

The angular velocity of a turntable-man system determines the rate at which the man is rotating. As the angular velocity increases, the man will experience a greater centripetal force and may have difficulty maintaining balance.

5. How can angular velocity be changed in a turntable-man system?

Angular velocity in a turntable-man system can be changed by changing the speed of rotation of the turntable or by changing the distance between the man and the axis of rotation. It can also be changed by applying an external torque to the system.

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