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Fidget spinner

What is the moment of inertia of a fidget spinner assuming mass of the spinner as M and radius of the disc end as \(R\)? (Assuming that the Fidget spinner is made of three discs )

Note by Adharsh M
3 weeks, 6 days ago

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In that case, how about posting this as a question ? Adharsh M · 3 weeks ago

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so added up all moment of inertia of all the discs along the axis at origin right? Adharsh M · 3 weeks ago

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@Adharsh M Yes, that's right. If you agree with my answer, you can post it. Thanks Steven Chase · 3 weeks ago

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Actually, there is also one disc with centre at the origin. Adharsh M · 3 weeks, 1 day ago

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@Adharsh M In that case it's easier. \(\frac{25}{2} M R^2\) Steven Chase · 3 weeks, 1 day ago

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Mr.Steven Chase please post your solution. Adharsh M · 3 weeks, 3 days ago

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@Adharsh M

Model the fidget spinner as three disks with their centers as the vertices of an equilateral triangle. The disk radius is \(R\) and the distance (\(d\)) of each disk center to the origin is \(\frac{2}{\sqrt{3}} R\).

The moment of a disk of mass \(M\) about it's center is \(\frac{M R^2}{2}\). Since all three disks are the same distance from the origin, consider the total mass to be concentrated in one of them. We must use the Parallel Axis Theorem to calculate the moment with respect to the origin.

\[I = \frac{M R^2}{2} + Md^2 = \frac{M R^2}{2} + \frac{4}{3} MR^2 = \boxed{\frac{11}{6} MR^2} \] Steven Chase · 3 weeks, 2 days ago

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there are no holes and the discs are stuck together using an adhesive. Adharsh M · 3 weeks, 3 days ago

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@Adharsh M I have an answer. This is a pretty nice problem. If you have the answer, perhaps you could post it as a problem. Steven Chase · 3 weeks, 3 days ago

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it should consits of only three discs of each radius R and mass of each disc as M/3 Adharsh M · 3 weeks, 3 days ago

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@Adharsh M Do the disks have holes in them? If so, what are the inner and outer radii. And how are the disks connected to each other? If you look at an actual fidget spinner, there is a complicated connection between them. We'll probably need to simplify the connection. Steven Chase · 3 weeks, 3 days ago

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How exactly do you want it to be modeled? Steven Chase · 3 weeks, 4 days ago

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