Conservation of Angular Momentum Experiment: Moment of Inertia

[chrismoon]

Homework Statement

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?

Homework Equations

I_disk=(1/2)(Mass)(radius)²
I_{hoop/hollow cylinder}=(Mass)(radius)₂
L_i=I_diskω_{disk initial}
L_f=(I_disk+I_{hoop/hollow cylinder})ω_{combined final}

The Attempt at a Solution

First, I calculated the moments of inertia-
I_disk=(1/2)(Mass)(radius)²=(1/2)(0.915kg)(0.253m/2)²=0.00732kgm²

I_{hoop/hollow cylinder}=(Mass)(radius)²=(0.708kg)(0.125m/2)²=0.00277kgm²

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

The I_combined 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 (I_disk+I_{hoop/hollow cylinder}) to calculate a percent error.

 

[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.

 

[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.