A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 0. A string is attached to the cylinder so that the cylinder can roll without slipping on the incline. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string. (Solid disk or cylinder: Içm =MR2) (a) Draw all forces acting on the cylinder, the pulley, and the block. (b) Write Newton's second law (translation, and/or rotation) for the motion of each object after the system is released from rest. (c) Find the magnitude of the acceleration of the block in terms of g, and 0.

The assembly shown in the figure below consists of a thin rod of length { = 22.4 cm and mass m = 1.20 kg with a solid sphere of diameter d = 10.0 cm and mass M = 2.00 kg attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise. (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in J)? (b) What is the angular speed (in rad/s) of the rod and sphere? rad/s (c) What is the linear speed (in m/s) of the center of mass of the sphere? m/s (d) How does it compare with the speed had the sphere fallen freely through the same distance of 27.4 cm? (Express your answer as a percentage.) %. is ---Select--- V swing v Vall by