A uniform cube of mass M and side length L (all sides have the same length) is free Hoating in space. At time = (), it is stationary at 0 and its orientation is fixed but not given. At t = 0, a particle of mass m is located at hy and moving with velocity ux. The particle and the cube collide elastically (the kinetic energy of the system is conserved) at = (. You may neglect all the forces acting between the cube and the particle except during the short collision. You may also neglect all external forces. a) Show that the inertia tensor of the cube Igy = %.-'I.rf I2I; . does not depend on its orientation (you may use this fact in later parts even if you can not prove it). b) Compute the linear momentum, angular momentum about 0, and the kinetic energy of the system before/after the collision. c) Express the linear momentum, angular momentum about 0, and kinetic energy of the system in terms of the velocity of the cube after the collision Uep We v = |vy |, the angular velocity of the cube after the collision w = |w, |, the = 'z W, velocity of the particle after the collision w = jw, |, as well as M, m, L. W d) Use conservation of momentum to express v,, vy, v.,Ww,,wy, w; in terms of wy,wy, w., M,m,L, h, u. e) In this part only, you are given that m = %M' = %L. Find the maximum possible w. with which the particle can be reflected up after the collision with the cube