How is the moment of inertia related to the square of the distance?

[Hardik Batra]

Moment of inertia is
I = MR²
object has more mass means more inertia and less mass means less inertia.
That means moment of inertia is directly proportional to mass.
But how the moment of inertia is directly proportional to the square of the distance.?

 

[Doc Al]

Moment of inertia is
I = MR²

For a point mass, not in general.

object has more mass means more inertia and less mass means less inertia.

OK.

That means moment of inertia is directly proportional to mass.

Only if the distance to the axis--the R--is fixed.

But how the moment of inertia is directly proportional to the square of the distance.?

It's a measure of the torque required to produce a given rotational acceleration. Loosely: The further the mass is from the axis, the harder it is to get it to rotate.

 

[Hardik Batra]

but why it is square of the distance rather than only distance.

 

[Doc Al]

but why it is square of the distance rather than only distance.

Give this a look: http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#rlin

 

[Hardik Batra]

Thanks. It helpful for me.