Four identical particles of mass 0.60 kg each are placed at the vertices of a 2.5 m ✕ 2.5 m square and held there by four massless rods, which form the sides of the square. (

a) what is the rotational inertia of this rigid body about an axis that passes through the midpoints of opposite sides and lies in the plane of the square?

(b) what is the rotational inertia of this rigid body about an axis that passes through the midpoint of one of the sides and is perpendicular to the plane of the square?

a)

b)

Explanation:

Given:

mass of four identical particles placed on the vertices of 2.5 m square,

a)

Now, when the square frame is mass-less and the axis of rotation passes through the plane of the square from the midpoints of the opposite sides then we have 4 point masses rotating about the axis.

So, rotational inertia of the system:

b)

When the axis of rotation passes through the midpoint of one of the sides of square and is perpendicular to the plane of the square we get one pair at a certain  distance and the other pair at some other certain distance as shown in the schematic.