Question

Four equal masses m are located at the corners of a square of side L, connected by essentially massless rods. Find the rotational inertia of this system about an axis

(a) that coincides with one side and
(b) that bisects two opposite sides.
(a) Ia=?
(b) Ib=?

Answer 1

Moment of Inertia: It is the property of an object that measures, how much an object can resist it's rotational motion.

We have 4 masses at the corner of square of length L. The formula of moment of inertia will be

I = m
`L^(2)`

Finding the Rotational Inertia of this system

(a) that coincides with one side (Ia):

The moment of inertia of each of the two sides is

I = m
`L^(2)`

so, both sides will have the moment of inertia equals to

I = 2m
`L^(2)`

(b) that bisects two opposite sides (Ib):

The distance of all four masses from the axis= L/2

so, the moment of inertia of all four masses will be

I =4m
`(L/2)^(2)`

I =4m
`(L^(2))/4`

The final value will be

I = m
`L^(2)`