What is the Moment of Inertia for a Hollow Torus?

[raj26]

I would like to know the formula for Moment of inertia for horizontal rotation of circular tube(i.e wheel) of mass 65kg, wheel dia=2m, tube dia=0.1m.

 

[K^2]

Moments of inertia. From your description, you want the one for torus.

 

[raj26]

But is the formula you have told applies for rotation around a horizontal axis? The figure shown in wiki is for vertical configuration.

 

[K^2]

There are 3 principal axis. 2 of them have the same moment of inertia about them. The page I linked to gives you two formulae. You can use these to derive expression for ANY axis.

 

[raj26]

Thanks for your answers...Actually i needed MOI for a hollow torus ...I got the two MOI expressions.

O

 

[K^2]

For hollow torus, take MOI for solid torus with outer radius, and subtract solid torus of inner radius. MOI is additive, so this should give you correct answer. Just keep in mind that the mass would be greater if the torus was solid. You need to account for that.

 

[raj26]

One last Q: I verified your answer for the case of solid torus on the net and found that horizontal axis MOI and the diameter axis MOI are the same. Can i assume the same for a hollow torus. (Again i have MOI for it for two axes and i need for the horizontal one!)