Rolling

Pure Rolling Without Slipping

Consider a wheel that rοlls on a surface, without slipping, as shown below.


rolling wheel


Where:

α is the angular acceleration of the wheel, in radians/s2

w is the angular velocity of the wheel, in radians/s

r is the radius of the wheel

V is the linear velocity of the geometric center of the wheel

a is the linear acceleration of the geometric center of the wheel

Thus,


equations for rolling without slipping


Rοlling With Slipping

In the case of rοlling with relative slipping, there is relative sliding at the contact between wheel and surface. This means that


equations for rolling with slipping


Dynamics problems that involve rοlling with relative slipping are more complicated than problems that involve pure rοlling. This is because you have to account for the direction of slip in order to determine the direction of (kinetic) friction, at the contact surface. To see an example of a solved problem that involves rοlling with relative slipping, see The Physics Of Billiards. Scroll down near the end of the page to the section entitled: "Physics of Billiards — A Closer Look At Relative Slipping". In this section, general equations are given for rοlling with relative slipping, on a flat surface. It is useful to study this section, and then use the results for similar problems that you run into.



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