Question

A massless horizontal bar (in blue) is free to rotate about the axis as shown. It rotates at a constant $\omega$. Each of the masses (in red) is 7 kilograms, and can be affixed at various positions along the bar. By what factor does the moment of inertia of the system decrease, if the masses are moved from their original positions 0.9 meters away from the axis to final postions 0.65 meters away from the axis?

Answer 1

initial moment of inertia Ii = 2( mr^2) = 2 x 7 x 0.9^2 = 11.34 kg m^2

finally moment of inertia If = 2 x 7x 0.65^2 = 5.915 kg m^2

If / Ii = 5.915 / 11.34 = 0.522 .......Ans