There’s a difference between a spherical cow, an internally homogenous spherical cow, and a rigid, internally homogenous spherical cow. The typical spherical cow is said / written as the first type but is actually assumed to be the third type.
The closer we look, the more these details matter.
Eggs are a particularly fun example that’s readily to hand. The easiest way to tell if an egg is hard boiled is to spin it on your kitchen counter. Taking care not to let it fall off to the floor in case you’ve guessed wrong about it being hard boiled.
It depends quite a bit on the rigidity of the ball and the tracks as well. Rolling resistance is, more than anything else, a function of how much the rolling body and the surface deform under the weight of the rolling body,
This is primarily what I had in mind when I posted. It would seem that two bearing of the same dimension but different weight would have different rolling resistance because of deformation.
I remember an Ontario Science Center demo - from 40 years ago or more, not sure if it’s still there. They dropped a steel ball bearing on a steel plate - slightly concave to keep the bouncing bearing from straying off the plate. It had a fairly good bounce - probably 90% or more, not what we’d expect with steel. It bounced for probably half a minute when dropped from a meter. Steel does not deform much, I would imagine rolling resistance is a minor factor. this is why roller coasters can run for a long time with one drop - probably rolling resistance with steel wheels on steel tracks is close to negligible, the biggest drag is air resistance. (I assume it was a form of spring steel where the deformation of ball hitting a plate resulted in springiness -compression and rebound rather than heat)
the important point is - energy turned from gravitational potential energy due to height is converted to kinetic energy due to momentum and rotational momentum - but that same energy is recovered completely as the object rolls back uphill. (Minus rolling resistance, air resistance, and any spherical cows in the way)
My Engineering Math lecturer did that demonstration. Dropped a golf ball. Dropped a tennis ball. Dropped a blackboard duster he picked up off the lectern. Which had been loaded with touch powder by the engineering students. They had been expecting that he would just use it to clean the blackboard, to general hilarity. Instead, they got the single moment where every person in the theatre was paying attention and watching that object. Both less startling and more memorable.
