Question

Let I1 be the moment of inertia about the centre of mass of a thick asymmetrical body. Let I2 be the moment of inertia about an axis parallel to I1. The distance between the two axes is ‘a’ & the mass of the body is ‘m’. Find the relation between I1 & I2.

(a) I2 = I1 – ma^2

(b) I1 = I2 – ma^2

(c) I2 = I1

(d) Parallel axis theorem can’t be used for a thick asymmetrical body

I got this question by my school teacher while I was bunking the class.

I would like to ask this question from Theorems of Perpendicular and Parallel Axes in section System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Right option is (b) I1 = I2 – ma^2

To elaborate: Parallel axis theorem can be used for any body. The parallel axis theorem states that moment of inertia about an axis perpendicular to an axis passing through centre of mass is given by:

I = ICOM + ma^2, where m is mass of the body & ‘a’ is the distance between the axes. So, I2= I1 + ma^2 OR I1 = I2 – ma^2.