Find angular velocity using angular momentum

In summary, a 20kg girl stands on a large turntable 4m from its center. The turntable has a moment of inertia (about its roation axis) of 200kgm^2. Assume that the girl is a point mass. If the girl walks inwards to a radius of 3m and stops, what is the new angular velocity? Find the change in kinetic energy.
  • #1
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A 20kg girl stands on a large turntable 4m from its center. The turntable has a moment of inertia (about its roation axis) of 200kgm^2. Assume that the girl is a point mass.

a) Assume that the girl and turntable are rotating at 1 rad/s. If the girl walks inwards to a radius of 3m and stops, what is the new angular velocity?

b) Find the change in kinetic energy.

I got these two parts, but I am stuck with c and d



c) Assume that the turnable is initially stationary and the girl is at r=4m.

The girl starts walking in a circle around the turntable at a speed of 2m/s relative to the ground. Find the angular velocity of the turntable relative to the ground.

d) The girl starts walking in a circle around the turntable at a speed of 2m/sy relative to the turntable. Find the angular velocity of the turntable relative to the ground.


c) I got from part a that w_i = 1 rad/s and w_f 1.37 rad/s. I know that that I = 200 + mr^2

However, I have no idea what to do when she walks 2m/s. As she gets closer to the center, the turntable will spin faster. But I don't know what to do for c and d.
 
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  • #2
For c and d the girl is no longer rotating at the same rate as the table. Don't try to find a moment of inertia for the system. Treat the girl as one object and the table as a second object and think about their individual angular momenta. The total angular momentum of the girl/table system is conserved. This is directly analogous to a linear momentum problem of a person walking on a plank that is on a frictionless surface. Starting from rest, if one thing goes one way, the other thing goes the other way.
 
  • #3
For part c, you know the inital momentum is zero, that will be conserved. Set the angular momentum of the girl equal to the angular momentum of the turntable.

Edit: Wow, Dan you are all over the place.
 
  • #4
Thank you.
 

Related to Find angular velocity using angular momentum

1. What is angular velocity and how is it related to angular momentum?

Angular velocity is the rate at which an object rotates around a fixed point. It is directly related to angular momentum, which is the product of an object's moment of inertia and its angular velocity.

2. How is angular velocity calculated using angular momentum?

Angular velocity can be calculated by dividing the object's angular momentum by its moment of inertia. The equation is: ω = L/I, where ω is angular velocity, L is angular momentum, and I is moment of inertia.

3. Can angular velocity and angular momentum be negative?

Yes, both angular velocity and angular momentum can be negative. This indicates that the object is rotating in the opposite direction compared to the chosen positive direction.

4. How is angular velocity different from linear velocity?

Angular velocity is a measure of how fast an object is rotating, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

5. What are the units of angular velocity and angular momentum?

The units of angular velocity are radians per second (rad/s), while the units of angular momentum are kilogram-meter squared per second (kg·m²/s). These units can also be written as newton-meters per second (N·m/s).

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