The uniform ball of radius ρ and mass m is gently placed in the bowl B with inner radius R...

The uniform ball of radius ρ and mass m is gently placed in the bowl B with inner radius R and is released. The angle ϕ measures the position of the center of the ball at G with respect to a vertical line, and the angle θ measures the rotation of the ball with respect to a vertical line. Assume that the system lies in the vertical plane. Hint: In working the following problems, we recommend using the rϕ coordinate system shown.

Figure P7.58

Assuming that the ball rolls without slip, determine the acceleration of the center of the ball at G, the angular acceleration of the ball, and the force on the ball due to the bowl immediately after the ball is released.