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 )

#Mechanics

Easy Math Editor

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Comments

How exactly do you want it to be modeled?

Steven Chase - 3 years, 10 months ago

it should consits of only three discs of each radius R and mass of each disc as M/3

Adharsh M - 3 years, 10 months ago

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 years, 10 months ago

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

Adharsh M - 3 years, 10 months ago

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 years, 10 months ago

Mr.Steven Chase please post your solution.

Adharsh M - 3 years, 10 months ago

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 years, 10 months ago

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

Adharsh M - 3 years, 10 months ago

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

Steven Chase - 3 years, 10 months ago

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

Adharsh M - 3 years, 10 months ago

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

Steven Chase - 3 years, 10 months ago

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

Adharsh M - 3 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$