What Happens When a Yo-Yo Rolls Without Slipping?

[PhizKid]

I'm not sure what you mean. Direction of linear acceleration or of angular acceleration? CM velocity or CM linear acceleration?

Hi haruspex. I was referring to the linear acceleration and the linear (center of mass) velocity.

 

[haruspex]

Hi haruspex. I was referring to the linear acceleration and the linear (center of mass) velocity.

Starting from rest, the initial acceleration must have the same sign as the first nonzero velocity and the first nonzero displacement. You can see this by considering a velocity-time graph. Thereafter, the acceleration may change sign, making it, for a while at least, opposite in sign to the velocity.