# Rolling

For other uses, see Rolling (disambiguation).
Four objects racing down a plane while rolling without slipping. From back to front: spherical shell (red), solid sphere (orange), cylindrical ring (green) and solid cylinder (blue). The time for each object to reach the finishing line depends on their moment of inertia around the rolling axis. (Details, Animated GIF version)

Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.

Rolling is achieved by a rotational speed at the line or point of contact which is equal to the translational speed. When no sliding takes place the rolling motion is referred to as 'pure rolling'. In practice, due to small deformations at the contact area, some sliding does occur. Nevertheless, rolling resistance is much lower than sliding friction, and thus, rolling objects, typically require much less energy to be moved than sliding ones. As a result, such objects will more easily move, if they experience a force with a component along the surface, for instance gravity on a tilted surface; wind; pushing; pulling; an engine. Unlike most axially symmetrical objects, the rolling motion of a cone is such that while rolling on a flat surface, its center of gravity performs a circular motion, rather than a linear one. Rolling objects are not necessarily axially-symmetrical. Two well known non-axially-symmetrical rollers are the Reuleaux triangle and the Meissner bodies. Objects with corners, such as dice, roll by successive rotations about the edge or corner which is in contact with the surface.

One of the most practical applications of rolling objects is the use of Rolling-element bearings, such as ball bearings, in rotating devices. Made of a smooth metal substance, the rolling elements are usually encased between two rings that can rotate independently of each other. In most mechanisms, the inner ring is attached to a stationary shaft (or axle). Thus, while the inner ring is stationary, the outer ring is free to move with very little friction. This is the basis for which almost all motors (such as those found in ceiling fans, cars, drills, etc.) rely on to operate. The amount of friction on the mechanism's parts depends on the quality of the ball bearings and how much lubrication is in the mechanism.

Rolling objects are also frequently used as tools for transportation. One of the most basic ways is by placing a (usually flat) object on a series of lined-up rollers, or wheels. The object on the wheels can be moved along them in a straight line, as long as the wheels are continuously replaced in the front (see history of bearings). This method of primitive transportation is efficient when no other machinery is available. Today, the most practical application of objects on wheels are cars, trains, and other human transportation vehicles.

The velocity of a particle in the rolling object is given by: $\mathrm{v}=r\times\omega$, where $r$ is the distance between the particle and the rolling object's contact point (or line) with the surface, and $\omega$ is the rolling object's angular velocity.