Question

Four particles, one at each of the four corners of a square with 4.5-m-long edges, are connected by massless rods. the masses of the particles are m1 = m3 = 4.0 kg and m2 = m4 = 7.0 kg. find the moment of inertia of the system about the z axis.

Answer 1

Length of the square edges r = 4.5 m.
Mass of the particles at each corner is as follows
m1 = m3 = 4.0 kg and m2 = m4 = 7.0 kg
Moment of inertia I = m x r^2
So in this case I = r^2(m2+m1) + r^2(m2+m3)
=> I = 4.5^2(7 + 4) + 4.5^2(7 + 4) => I = 4.5^2 (11 + 11)
=> I = 20.25 x 22 = 445.5 kg m^2