A uniform solid cylinder of mass M and radius R is rolling without slipping on a flat horizontal surface. Let L_C be the magnitude of its angular momentum about its center of mass, and L_P be the magnitude of its angular momentum about a stationary point on the ground. The ratio L_P L_C is :

Step-by-step solution

For a uniform solid cylinder rolling without slipping with center of mass velocity v , its angular velocity is = v R . The moment of inertia of the solid cylinder about its center of mass is I_ cm = 1 2 MR^2 . The angular momentum about the center of mass is: 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 given by: L _P = L _ cm + r _ cm/P M v _ cm Since the cylinder is rolling, the direction of L _ cm and the cross product r _ cm/P M v _ cm are the sam