# How to proof mass moment of inertia formula for a hoop with axis across the diameter?

##
Moment of inertia of the hoop is given by:

#1/2mr^2#

How to proof that?

You may attach a hyperlink or write down the derivation from #I=mr^2# .

Thanks

Moment of inertia of the hoop is given by:

How to proof that?

You may attach a hyperlink or write down the derivation from

Thanks

##### 1 Answer

Jul 20, 2017

See the proof below

#### Explanation:

The volume is

The thickness is

The radius of the hoop is

The density is

The moment of inertia is

As the axis is across the diameter

The distance from the differential mass

Therefore, substituting in the integral, we integrate from