A solid uniform cylinder of mass M, height H and radius R is sliding in the r direction on a leveled surface (the normal to the surface is z, which is also the direction of gravity). The cylinder is rolling (while sliding) with angular velocity that remains aligned with the y axis. The inertia tensor of the cylinder about its center of mass is [M (H3+ 1R?) IOM = MR- 0 M (LH' + 1R-) The kinetic coefficient of friction between the ramp and the cylinder is /. a) Draw a free body diagram, denote and compute all forces. Note that you can only find the kinetic friction force up to a sign at this point. b) Given and velocity row = ux and angular velocity w = wy at some time t, find a and w and that time. c) Given w(0) and u(0), find w(t) and u(t) at all times. d) Compute the quantity Ex = =Mrow row + :w . (Icww) as a function of time (Ex is known as the kinetic energy). If your answer to (c) is correct, Ek will turn to be non-increasing even for large t