Thread: What is the rotational inertia of a ball rolling back and forth in a cylindrical trough?

I'm a little confused-- seems more complicated than just plugging into the parallel-axis theorem. I suppose this gets into the realm of a pendulum?

Say you know the radius of the ball and the radius of the 'cylinder' (though only part of the cylinder makes up the trough), as well as the mass of the ball. How would you arrive at a value for total moment of inertia?

without doing the calcs I'd suggest you look at the total energy.
The energy when it is stationary is all gravitational potential energy.