A uniform hollow semi-cylindrical shell of mass m and radius a is rocking from side to side without slipping on a horizontal surface (as shown in the figure).

l) A uniform hollow semicylindrical] shell of mass m and radius a is rocking from side to side without slipping on a horizontal surface (as shown in the gure}. Show that in the small angle approximation min2) g - the period of the oscillations is equal to 231 You can solve this problem in following steps: - show that the kinetic energy of the system can be written as T = mqiz (a2 +A2-2ad cos )+%IEZM12 (the rst term is due to the motion of the center of mass, and the second term is due to the rotation of the shell about its center of mass). Compute A as a function of a (note that the triangle formed by P, CM and the symmetry axis of the shell is not a right triangle in general, even though it looks so on the diagram); - nd IE2\