3. Without friction, would a ball still spin when going down a slope?

Without friction, would a ball still spin when going down a slope?

Good question. It does not assume that the ball is symmetric because it does not matter where the ball's center of mass is. If there is friction, it will rotate.

Look at this diagram. Let's first assume that there is no friction. At the center of this diagram, we find the center of mass. There are two forces acting upon the center of mass. First, there is gravity (which we split into two components, the green vectors) and there is the normal force (the red vector perpendicular to the surface). If you add these vectors together, you'll find that the net force acts parallel to the slope, and this will cause the ball to move down the slope. You calculate the motion of the ball at its center of mass. No matter where it is, you will always get a net force parallel to the slope.

Now let's add friction to the equation. We have already established that the ball is moving down the slope, calculated at its center of mass. Let's imagine that we now have a pivoted bar that has one end where the ball contacts the slope, where its pivot point is, and another end at the ball's center of mass. Do you remember that we have a net force parallel to the slope? This force will drag the bar in a counter-clockwise fashion in our situation the diagram depicts. This is where the rotation comes from! Don't think too much into this bar analogy though, it's just a thought experiment used to help you understand where the torque is coming from. I could expand the analogy a bit more if you want but it will get pretty complicated. The point is that if you think about it, it doesn't matter where the center of mass it, the ball will always rotate if there is friction.

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