Question

Moment of inertia of a uniform ring of mass m and radius r about its tangent lying in its own plane is

Answer 1

• Moment of inertia of a uniform ring of mass m and radius r about its tangent lying in its own plane is 3/2 MR²

Given-

• Mass of the ring = M

• Radius of the ring = R

Tangent is drawn in the attached figure-

AB is the tangent and XY is the diameter of the ring.

By using the parallel axis theorem

I (AB) = I (XY) + MR²

And we know that moment of inertia about its diameter is 1/2 MR²

By putting the value we get

I (AB) = 1/2 MR² + MR² = 3/2 MR²