# B Moment of inertia for a fidget spinner...

1. Jun 12, 2017

### Isaac0427

Hi,
I was just curious, how would you go about calculating the moment of inertia for a fidget spinner? I was thinking about it, and I don't know how to calculate moment of inertia for weird shapes like that.
Thanks!

2. Jun 12, 2017

### scottdave

This is a great question. What if you could do some experiments to give and idea of what it is similar to? I have some ideas. Let me do some thinking and I'll get back with you on this.

3. Jun 12, 2017

### scottdave

So this is what I'm thinking. Most of the weight of a fidget is in the 4 circular bearings: one at the center and one at the end of each arm. Calculate the moment of one of the circular bearings.
From this ( http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html ) you can get the moment of a hollow cylinder as Ibearing = (1/2)*M*(b^2 + a^2), where a & b are radii to the inner start of metal and outer edge of metal. Then use the parellel axis theorem. Take a look at this: http://emweb.unl.edu/NEGAHBAN/EM223/note19/note19.htm and scroll down to the part about parallel axis. So the moment of each outer bearing is Ibearing + m*d2.
To estimate the mass of each bearing, weigh the entire fidget and divide by 4. If it has bearings which can pop out, then you could weigh them individually.

OK so how can we experimentally test this? One idea I had was to put your fidget inside of a can, which doesn't weigh much and then roll it down an incline, then compare how that rolls to how other cylinders with known moments will roll.

Another thought: (more difficult) If you could connect a gyroscope of known moment one the same axis, then you could spin them in opposite directions and try to cancel out the angular momentums. The difficulty here is determining exactly how fast each thing is spinning.

4. Jun 12, 2017

### Drakkith

Staff Emeritus
I think you'd need to be able to put the shape and density of the object in terms of a couple of equations that you can then integrate with calculus. A decent approximation may be to reduce the shape of the object to several simpler objects like cylinders and disks. Once you do that, finding the moment of inertia is relatively easy if I remember my physics course correctly.

5. Jun 13, 2017

### vanhees71

I'd also recommend to measure it ;-).

6. Jun 13, 2017

### CWatters

You can add moments of inertia about the same axis. So the usual trick is to divide the object into simpler shapes. Sometimes you can just look up equations for those simpler shapes.

The parallel axis theorem allows you to calculate the MOI of a simple shape that isn't rotating about the usual axis. Eg a wheel rotating about a point on the rim rather than its centre.