Two heavy particles having masses `m_(1)` and `m_(2)` are situated in a plane perendicular to line `AB` at a distance or `r_(1)` and `r_(2)` respectively.

a. What is the moment of inertia of the system about axis `AB`?
b. What is the moment of inertia of the system about an axis passing through `m_(1)` and perpendicular to the line joining `m_(1)` and `m_(2)`?
c. What is the moment of inertia of the system about an axis passing through `m_(1)` and `m_(2)`?

Explanation

a. Moment of inertia of the particle on the left `I_(1)=m_(v)r_(1)^(2)`,. Moment of inertia of the particle on the right is `I_(2)=m_(2)r_(1)^(2)`.
Moment of inertia of the system `AB` is `I=I_(1)+I_(2)=m_(1)r_(2)^(2)+m_(2)r_(2)^(3)`
b. Moment of inertia of the particle on the left is `I_(1)=0`.
Moment of inertia of the particle on the right is `I_(2)=m_(2)(r_(1)+r_(2))^(2)`.
moment of inertia of the system about the given axis is
`I=I_(1)+I_(2)=0+m_(2)(r_(1)+r_(2))^(2)`
c. Moment of inertia of the particle on theleft is `I_(1)=0` Moment of inertia of the particle on the right is `I_(2)=0`
Moment of inertia of the system about the given axis is `I=I_(1)+I_(2)=0+0`