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.

Question

Physics

Julissa Hayes

13 June, 15:23

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.

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Garrett Dorsey · 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