The device shown in the figure below consists of a thin rod of lengthlf = 23.7 cm and mass m = 1.20 kg with a solid ball of diameter d = 10.0 cm and mass M = 2.00 kg attached to its top. The device is free to pivot about a frictionless axle through the bottom of the rod. The device is initially vertical and at rest when it starts to rotate clockwise. l r! .11 4- in (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in J)? |:]J (b) What is the angular speed (in rad/s) of the rod and ball? :1 rad/s (c) What is the linear speed (in m/s) of the center of mass of the ball? :i m (d) How does it compare with the speed had the ball fallen freely through the same distance of 28.7 cm? (Express your answer as a percentage of Vfall') szing is Vfall by Z] %' A hanging weight, with a mass of m1 = 0.375 kg, is attached by a rope to a block with mass m2 = 0.825 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is ,uk = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. li'.' 1:1 \"30 '2 9' V m i k?) (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. :1 m (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? :1 ram