Q1 A string is wound around uniform cylinder of radius R and mass M. The cyclinder is released from rest with the string vertical and its top tied to a fixed bar and falls through a distance h. (4gh/3) 1/2 a. Using a conservation of energy argument, show that the speed of the center of mass is b. Using a kinematic equation for motion with uniform acceleration, show that the magni- tude of the acceleration of the cylinder is 2g/3. C. Show that the tension in the string is one-third of the weight of the cylinder. Q.2 A door of width 1 m is initially at rest, parallel to the i direction with a hinge at the origin. The door has a mass of 20 kg- a. Calculate the moment of inertia of the door. b. A force F = i+ 3j + 0k (in newtons) is applied at the position 7 = 0.82 + 03 + 0k (in meters). Calculate the torque 7 on the door. c. Calculate the angle between the force and the door in its initial position. d. Calculate the initial angular acceleration of the door. Q.3 A top-load washing machine has clothes distributed evenly about the center of a drum initially at rest, and has a moment-of-inertia of 2.5 kg m. An electric motor delivers constant power as the angular speed follows the equation: W = 40tz (1)a. Calculate the angular acceleration after 1 second. b. Calculate the torque after 1 second. c. Calculate the average power provided by the motor over this period. Q 4. From first principles, show that the moment of inertia of a uniform solid sphere is: I = MR (2 ) Q5. Calculate and compare the rotational kinetic energy of the Earth and the orbit of the Moon