Conservation of Angular Momentum Experiment: Moment of Inertia

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
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}

3. 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.