(adsbygoogle = window.adsbygoogle || []).push({}); 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_{disk}ω_{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}=0.00732kgm^{2}

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

I_{combined}=(0.00732kgm^{2})+(0.00277kgm^{2})=0.01009kgm^{2}

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.

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# Homework Help: Conservation of Angular Momentum Experiment: Moment of Inertia

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