To define such a motion we have to relate the translation of the object to its rotation.

For example, let’s consider a wheel (or cylinder) rolling on a flat horizontal surface, as shown below.

Where:

The wheel rolls without slipping only if there is no horizontal movement of the wheel at the contact point

Now, if the wheel (shown above) were moving either right or left, but with no rotation, the wheel would skid along the surface. And as a result, the contact point

Therefore, we deduce that the wheel must rotate (at a certain speed) for there to be no skidding on the surface.

To begin the analysis set up a schematic as shown below, along with sign convention.

Where the following additional variables are introduced:

Therefore, by vector addition the velocity of point

Now, for rotational motion:

For no skidding

As a result,

For the case of rolling without slipping, this is the equation relating the velocity of the geometric center of the wheel

If we differentiate the above equation with respect to time we get:

For the case of rolling without slipping, this is the equation relating the acceleration of the geometric center of the wheel

Equations (1) and (2) also apply for curved surfaces. In other words, even if the rolling surface were curved, the velocity of contact point

For many dynamics problems, rolling without slipping means there is a friction force acting on the wheel at the contact point

For the case of rolling with slipping, equations (1) and (2) do not apply, and there is no relationship between the velocity (and acceleration) of the geometric center

To see examples of problems involving rolling (with and without slipping) see Physics Of Billiards, and Physics Of Bowling.

Return to

Return to

Confused and have questions? Head over to Chegg and use code “CS5OFFBTS18” (expires 11/30/18) to get $5 off your first month of Chegg Study, so you can get step-by-step solutions to your questions from an expert in the field. Plus get a free 30 minute tutoring session.

Are you an employer looking for someone with a physics degree?

Do you want exposure for your physics article or publication?

Consider advertising on this website. It has over 100,000 unique visitors a month. Click here for more information.