Four point masses lie at the corners of a rectangle with sides of length 3 m and 4 m ., as shown in figure . Find the moment of inertia about of the diagonals . Take M = 1 kg .

Explanation

For each mass we need its perpendicular distance from the axis . For each axis , two masses do not contribute to the moment of onertia . The other two are at the same diatance M .
AB = 4m , BC= 3 m , AC = 5 m
In `triangle ABC sin theta = (BC)/(AC) = 3/5`

In `triangle BNA sin theta = x/4 rArr 3/5 = x/4 rArr x = 2 . 4m `
`I_(A) = (4kg) (2.4m)^(2) +(2kg) (2.4 m)^(2) = 34.6 kgm^(2) `
`I_(g) = (1kg) (2.4m)^(2) +(3kg) (2.4 m^(2)) = 23.0 kgm^(3)`