A uniform solid cylinder of mass M and radius R is rolling without slipping on a flat horizontal surface. Its centre of mass moves with a constant speed v . If L_C is the magnitude of its angular momentum about its centre of mass and L_P is the magnitude of its angular momentum about a stationary point P on the ground, the ratio L_C L_P is:

Step-by-step solution

For a solid cylinder rolling without slipping, the angular velocity is = v R . The angular momentum about the centre of mass is given by: L_C = I_ cm = ( 1 2 MR^2 ) ( v R ) = 1 2 MvR The angular momentum about a stationary point P on the ground is the sum of the angular momentum about the centre of mass and the angular momentum of the centre of mass about P : L _P = L _C + r _ cm M v _ cm Since the cylinder is rolling on the ground, the perpendicular distance from P to the line of motion of the centre of mass is R