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What will be the moment of inertia of a semi-circular ring about an axis which is perpendicular to the plane of the ring and passes through its centre?

What will be the moment of inertia of a semi-circular ring about an axis which is perpendicular to the plane of the ring and passes through its centre?

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Using Parallel Axis Theorem
I0=ICM+Md^2
where Io= Moment of inertia about centre=MR^2
and ICM= Moment of inertia about centre of mass

d=2R/π(distance between centre of mass and centre)

ICM=I0−M(2R/π)^2
=MR^2[1−4/π^2]

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