A half-circular cup with radius r rotates about an offset axis with constant rate ω. The motion allows the ball to stay at a position θ in steady state. If the final angle is θ = 40 degrees
a. Calculate the time it takes for the ball to reach the final angle θ = 40 degrees
b. Determine the velocity of the ball at the final angle θ = 40 degrees
c. Find the acceleration of the ball at the final angle θ = 40 degrees
d. Calculate the displacement of the ball from its initial position to the final angle θ = 40 degrees