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chrismoon
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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
Idisk=(1/2)(Mass)(radius)2
Ihoop/hollow cylinder=(Mass)(radius)2
Li=Idiskωdisk initial
Lf=(Idisk+Ihoop/hollow cylinder)ωcombined final
The Attempt at a Solution
First, I calculated the moments of inertia-
Idisk=(1/2)(Mass)(radius)2=(1/2)(0.915kg)(0.253m/2)2=0.00732kgm2
Ihoop/hollow cylinder=(Mass)(radius)2=(0.708kg)(0.125m/2)2=0.00277kgm2
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.