What is parallel and perpendicular axis theorem and how to use them?

Question

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be:

a)I

b)3I

c)6I

d)8I

Also explain how to use parallel axis theorem. Thanks in advance!!!

Answer 1

(a) Parallel axes theorem

The moment of inertia I of a body about any axis is equal to the moment of inertia I_G about a parallel axis through the centre of gravity of the body plus Mb², where M is the mass of the body and b is the distance between the two axes. (See Figure 1)

I = I_G + Mb²

 

(b) Perpendicular axes theorem

For any plane body (e.g. a rectangular sheet of metal) the moment of inertia about any axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane of the body which intersect the first axis in the plane.
This theorem is most useful when considering a body which is of regular form (symmetrical) about two out of the three axes. If the moment of inertia about these axes is known then that about the third axis may be calculated.

I_a = I_b + I_c

Answer 2

Correct answer to your objective question is (C) i.e 6I