# Conservation of Angular Momentum Experiment: Moment of Inertia

1. Jul 29, 2012

### chrismoon

1. The problem statement, all variables and given/known data
I did a lab where there was a rotating solid disk with mass= 0.915kg and diameter=0.253m.
This was rotating horizontally with an initial angular velocity of 3 different values ω radians/second. After recording the initial angular velocity, I dropped a thin-walled hollow cylinder with mass=0.708kg and diameter=0.125m in the center and measured the final angular velocity, testing the conservation of angular momentum.

Issue: If I placed the ring off center of the disk by say, 1cm (0.01m), how will that affect my moment of inertia?

2. Relevant equations
Li=Idiskωdisk initial
Lf=(Idisk+Ihoop/hollow cylindercombined final

3. The attempt at a solution
First, I calculated the moments of inertia-

Icombined=(0.00732kgm2)+(0.00277kgm2)=0.01009kgm2

The Icombined is for the ideal situation of the ring being completely centered, but I have no idea what I would do to get the experimentally flawed moment of inertia. Would I just change the radius of the hoop/cylinder by 1cm? If so, would I add or subtract? I'm really not sure how I'd calculate it. I understand this all generally pretty well, but executing this has me a little stumped. I need a way to get the new final moment of inertia instead of the ideal (Idisk+Ihoop/hollow cylinder) to calculate a percent error.

2. Jul 29, 2012

### TSny

Hi, chrismoon. Have you studied the "parallel axis theorem"? You can use it to calculate the moment of inertia of the hollow cylinder when it is placed off-center on the disk.

3. Jul 29, 2012

### pgardn

have you used the parallel axis theorem?

ok then...

late again, sorry. Its getting strange how I am right behind Tnsy.

I will now bow out again.

Last edited: Jul 29, 2012