Rolling Object going up a FrictionLESS Hill

Rotations can be challenging, but over time hopefully things start to click a bit more and make a little more sense. Here is one of those strange examples of a 'what if' situation: a ball rolling without slipping on a flat surface, but then going up a frictionLESS incline. What would this look like? Are there any differences from what we are used to seeing, which is something rolling without slipping even up the incline.

In everyday life, we are used to seeing something roll up a hill and both stop moving linearly as well as stop spinning at its maximum height. Would this happen if there is no friction on the hill?

The answer is NO...at the maximum height, the linear motion stops, that much we know. But here is the kicker: without friction between the ball and the surface it sits on, there is no torque. Without torque, there is no change in the rotational motion of the object. In other words, the ball will still be spinning with the same angular velocity as it had at the bottom of the hill! It would look weird.

What's more, the ball would then start to move back down the hill, since a component of gravity produces a net force. As it accelerates linearly down the hill, the spin is opposite what we would normally see since that original spin has not at all changed! Very odd! Check out this in a bit more detail.