# Circular disk rotates with student on it

• bearhug
In summary: The correct initial value should be Li = (1/2)(150+60)(2.0^2)(1.5) = 1260In summary, a 150 kg platform with a radius of 2.00 m and a 60 kg student rotating on a frictionless bearing around a vertical axle with an angular speed of 1.5 rad/s. When the student moves 0.50 m towards the center, the angular speed of the system is 2.0 rad/s. The student's movement does not necessarily slow down the angular speed, as demonstrated in other forms of rotational motion. The initial value for rotational inertia was computed incorrectly, but after correction, the correct initial value is 1260.
bearhug
A horizontal platform in the shape of a uniform circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 150 kg, and radius of 2.00 m. A 60kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.5 rad/s when the student starts walking, what is the angular speed when she is 0.50 m from the center?

I originally used the equation Li=Lf
where Li= Iw= (1/2)(MR^2)wi which equals (.5)(210kg)(2.0^2)(1.5rad/s)
Li= 630
Lf= (If1+ If2)(wf)
=[(.5)(150)(2.0^2) + (60)(0.5^2)]wf
This gave me wf= 2.0 rad/s but that doesn't seem to make sense wouldn't the angular speed slow down as the student went closer to the center? Any hints as to where I went wrong is greatly appreciated.

Angular velocity wouldn't necessarily slow down as you go towards the center. Ever watch figure skating where a skater starts a spin with his legs/arms extended and as he brings his arms/legs closer he begins to spin much quicker? Ever watch divers do multiple flips, they bring as much mass as possible close to their axis of rotation to spin fast then when they want to stop they extend their arms and legs to finish the dive.

bearhug said:
I originally used the equation Li=Lf
where Li= Iw= (1/2)(MR^2)wi which equals (.5)(210kg)(2.0^2)(1.5rad/s)
You have computed the wrong initial value for I of the system, which will give you a wrong value for Li.
Li= 630
Lf= (If1+ If2)(wf)
=[(.5)(150)(2.0^2) + (60)(0.5^2)]wf
This time you computed the final rotational inertia properly. (Fix your initial value accordingly.)
This gave me wf= 2.0 rad/s but that doesn't seem to make sense wouldn't the angular speed slow down as the student went closer to the center?
What happens to the rotational inertia of the system as the person moves closer to the center? (Does it increase or decrease?) Then consider that L = Iiwi = Ifwf.

Thanks for the advice. Since only the initial value is incorrect I am under the impression that it is the Mass that is wrong. Originally I included both the student and the platform in the mass because I interpreted the problem as the student already being on the platform at the beginning. However that doesn't seem to be giving me the correct initial. So is that because the student isn't actually on the platform in the beginning? Thanks

The student is on the platform from the beginning. For some reason, when calculating the intial rotational inertia of the system you just added the masses instead of adding the rotational inertias of disk and student.

## 1. How does the circular disk rotate with the student on it?

The circular disk rotates with the student on it due to the principle of conservation of angular momentum. When the student initially jumps onto the disk, they impart a force that causes the disk to start rotating. As the student moves towards the center of the disk, the radius decreases and the rotational speed increases, allowing the disk to maintain its angular momentum.

## 2. What factors affect the rotation of the disk with the student on it?

The rotation of the disk with the student on it can be affected by the mass and speed of the student, as well as the radius and mass distribution of the disk. The distance of the student from the center of the disk also plays a role in the rotation.

## 3. Can the direction of the rotation of the disk be changed with the student on it?

Yes, the direction of rotation can be changed by applying an external force in the opposite direction of the current rotation. This force must be strong enough to overcome the angular momentum of the disk and the student.

## 4. Is it possible for the disk to continue rotating indefinitely with the student on it?

No, the disk will eventually slow down and come to a stop due to the effects of friction and air resistance. The rate at which it slows down will depend on the initial speed and mass of the student, as well as the surface of the disk and the surrounding environment.

## 5. Can the rotation of the disk with the student on it be used to generate electricity?

Yes, the rotation of the disk with the student on it can be harnessed to generate electricity through the use of a dynamo. The rotational energy of the disk can be converted into electrical energy, which can then be stored or used to power devices.

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