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 RR? (Assuming that the Fidget spinner is made of three discs )

Note by Adharsh M
2 years, 1 month ago

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How exactly do you want it to be modeled?

Steven Chase - 2 years, 1 month 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 - 2 years, 1 month ago

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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 - 2 years, 1 month ago

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there are no holes and the discs are stuck together using an adhesive.

Adharsh M - 2 years, 1 month ago

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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 - 2 years, 1 month ago

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Mr.Steven Chase please post your solution.

Adharsh M - 2 years, 1 month ago

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Model the fidget spinner as three disks with their centers as the vertices of an equilateral triangle. The disk radius is RR and the distance (dd) of each disk center to the origin is 23R\frac{2}{\sqrt{3}} R.

The moment of a disk of mass MM about it's center is MR22\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=MR22+Md2=MR22+43MR2=116MR2I = \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 - 2 years, 1 month ago

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Actually, there is also one disc with centre at the origin.

Adharsh M - 2 years, 1 month ago

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In that case it's easier. 252MR2\frac{25}{2} M R^2

Steven Chase - 2 years, 1 month ago

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so added up all moment of inertia of all the discs along the axis at origin right?

Adharsh M - 2 years, 1 month ago

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Yes, that's right. If you agree with my answer, you can post it. Thanks

Steven Chase - 2 years, 1 month ago

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In that case, how about posting this as a question ?

Adharsh M - 2 years, 1 month ago

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