A uniform solid cylinder is rolling without slipping on a horizontal surface. As shown in the figure, point A is at the highest position, point B is at the center of the cylinder, and point C is on the periphery at the same horizontal level as B . If v_A , v_B , and v_C represent the instantaneous speeds of points A , B , and C respectively with respect to the ground, which of the following relations is correct?

Step-by-step solution

For a cylinder rolling without slipping on a horizontal surface, the velocity of the center of mass is v_B = R , where is the angular velocity and R is the radius. The velocity of any point on the cylinder is the vector sum of the translational velocity of the center of mass and the tangential velocity due to rotation. For point A (at the highest position): The translational velocity is v_B (forward). The tangential velocity is R = v_B (forward). Thus, the speed of point A is v_A = v_B + v_B = 2v_B . For point C (o