A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle θ to the vertical and rolls without slipping. Model the motion of the sphere assuming no energy is lost, so it oscillates indefinitely. (the motion will be similar to a pendulum).
τ = Iα
I = (2/5)mr^2
N = normal force
α = angular acceleration
Theta is a small angle (approximations are acceptable)
The Attempt at a Solution
I attempted to model this similarly to a pendulum, but i just can figure out the torque. This is what i have so far :
not sure where to go from here, this is just the rotational motion of the ball i believe, but we need to account for the angular motion of the ball as it traverses the bowl.
Note: assume theta is a small angle as well.
Thanks in advance for the help !!