A slender uniform rod of length 0.80m and mass 2.5kg is rigidly connected at its free end to a point mass of 1.5kg. The composite system is hinged at the opposite end of the rod and is spun in a horizontal plane about the hinge with an angular speed of 6.0rads−1. The hinge is frictionless, and the masses remain in the horizontal plane during rotation.
(a) Determine the rotational inertia of the rod about the hinge axis.
(b) Determine the rotational inertia of the attached point mass about the same axis.
(c) Calculate the total rotational kinetic energy of the composite system at the stated angular speed.
(d) The motor driving the system suddenly doubles the angular speed. By what factor does the rotational kinetic energy of the system change? Justify your answer mathematically.