Question

If the moment of inertia of uniform circular ring of mass M and radius R about an axis through its center and perpendicular to its plane is I.Then moment of inertia of a uniform semi circular rung of mass M and radius R about axis through its center and perpendicular to its plane will be

Answer 1

The moment of inertia of a uniform semi circular ring through its center and perpendicular to its plane will be I cm = M R^2 [  1 - 4 / π^2 ]

Explanation:

We are given that:

• Mass of ring = M
• Radius of ring = R
• Moment of inertia = I

Solution:

using the theorem of parallel axis.

Io   = I  cm  +md^2

d = 2 r / π  [ d is the distance of centre of mass]

I cm = Io - m ( 2  R / π)^2

I cm = M R^2 [  1 - 4 / π^2 ]

Thu the moment of inertia of a uniform semi circular ring through its center and perpendicular to its plane will be I cm = M R^2 [  1 - 4 / π^2 ]