Rolling Motion of a Rigid Object

[Bashyboy]

Hello,

I am currently reading about what was given in the title of this thread. In my book, it discusses the motion of a cylinder rolling on a surface without slipping; the cylinder is rotating about an axis, and it's center of mass has translational motion. What exactly do they mean rolling without slipping? The book also mentions a relationship between the rotational and translation motion when there is no slipping, what would happen if there was slipping? Why wouldn't there be a relationship if there was slipping?

 

[Doc Al]

What exactly do they mean rolling without slipping?

Slipping means that the surfaces slide against each other; rolling without slipping means there's no sliding. The instantaneous speed of the point of contact with respect to the support surface is zero.

The book also mentions a relationship between the rotational and translation motion when there is no slipping, what would happen if there was slipping?

If the translational speed is just right compared to the rotational speed (v = ωr) then the surfaces will not slide or slip.

Why wouldn't there be a relationship if there was slipping?

There's no simple relationship if there is slipping.