Problem 1 A ball of mass m and radius R (moment of inertia I = mR...

 

Transcribed Image Text:

Problem 1 A ball of mass m and radius R (moment of inertia I = mR about its center) is released from rest at an angle o in a stationary spherical bowl of radius of curvature d+ R. The ball rolls on the bowl without slipping (in the plane of the diagram). (a) [25 points] Derive an equation of motion for the angle through the center of the ball, as defined in the figure. Solve this equation of motion for the case of 0 < < 1. (b) [15 points] What is the velocity of the center of the ball when 0 = 0 ? (Do not assume 0o < 1 here.) Problem 1 A ball of mass m and radius R (moment of inertia I = mR about its center) is released from rest at an angle o in a stationary spherical bowl of radius of curvature d+ R. The ball rolls on the bowl without slipping (in the plane of the diagram). (a) [25 points] Derive an equation of motion for the angle through the center of the ball, as defined in the figure. Solve this equation of motion for the case of 0 < < 1. (b) [15 points] What is the velocity of the center of the ball when 0 = 0 ? (Do not assume 0o < 1 here.)