# Rotating disk

1. Jul 25, 2010

### Gavroy

1. The problem statement, all variables and given/known data
Hey,
First, I want to say, if it is impossible for you to understand my text, which may be caused by the fact, that I do not speak english as my first language, please do not hesitate to ask me!
The problem definition is:
A disk with radius R rotates free in horizontal direction around its centre.
On the disk, there is a point mass m, which oscillates periodically around the centre of the disk. But the axis of oscillation from the point mass turns around the centre with the same velocity as the disk does.
The oscillation causes that the angular velocity of the disk changes with time.

Now, one should derive an equation which enables one to calculate the ratio of the masses (from the disk and the point mass) by using only data that can be worked out of a diagram which plots how the angular velocity changes with time.

I included two images which shows on the one hand the problem itself and on the other hand the diagram, we got to solve the problem.
2. Relevant equations

I just want to know whether you think that my approach is legitimate.

3. The attempt at a solution
I thought that one could use conversation of angular momentum in this case:
The moment of inertia of the point mass is:
I=mr2
I=mr2/2
Now I thought, I could say that I regard two "extreme cases"
1.) when the mass is at the centre of the disk
2.) when the mass is at the margin of the disk

Then I could use the maximum angular velocity and the minimum angular velocity w from the diagramm and calculate the ration of the masses by using the conservation of angular momentum by setting:
I(disk)*w max=I(disk)+I(point mass)*w min

cause in the first case the moment of inertia from the point mass is zero since the distance from the centre is zero.
and in the second the distance is equal to the radius from the disk.

Do you think my assumptions are all right?

(the diagram shows the angular velocity of the system varying by time )

#### Attached Files:

• ###### disk.JPG
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2. Jul 26, 2010

### hikaru1221

I haven't seen any assumption in your calculation, but it's correct, I think