This model applies to a single point particle moving in a circle of fixed radius (assumed to lie in the xy plane with its center at the origin) with constant speed. It is a subclass of the Rotational Motion model defined by

and r = R.

Usually uniform circular motion will be explicitly specified if you are to assume it. (Be especially careful of vertical circles, which are generally nonuniform circular motion because of the effects of gravity. Unless you are specifically told the speed is constant in a vertical loop, you should not assume it to be.) You can also use this model to describe the acceleration in instantaneously uniform circular motion, which is motion along a curved path with the tangential acceleration instantaneously equal to zero. This will usually apply, for example, when a particle is at the top or the bottom of a vertical loop, when gravity is not changing the speed of the particle.

• 1-D Motion (Constant Velocity)
• 1-D Motion (Constant Acceleration)

• tangential acceleration
• centripetal acceleration
• angular frequency

A single point particle.

The system must be subject to an acceleration (and so a net force) that is directed radially inward to the center of the circular path, with no tangential component.

• Free body diagram (used to demonstrate that a net radial force is present).
• Delta-v diagram.
• x- and y-position versus time graphs.
• θ versus time graph.