What is uniform circular motion?

Trajectory and constant speed

Uniform circular motion (UCM) is the motion of a point that travels around a circle of radius R at constant speed in magnitude (that is, at a speed whose value, in m/s, does not change). Watch out: the direction of the velocity vector changes constantly, since it always remains tangent to the circle. Only its magnitude ||v|| is constant.

Concrete examples: a point on the edge of a merry-go-round turning at a steady speed, a ball at the end of a string spun flat, or (as a first approximation) a satellite in circular orbit around the Earth.

Period and frequency

• The period T is the duration of one complete revolution, expressed in seconds (s).
• The frequency f is the number of revolutions per second, in hertz (Hz), with f = 1/T.

Linear speed

Since the point travels a distance of 2piR (the circumference of the circle) in a duration T, its (linear) speed is:

v = 2piR / T = 2piR*f

Quantity	Symbol	Unit
Radius	R	m
Period	T	s
Frequency	f	Hz
Speed	v	m/s

Classic pitfall: saying the motion is "uniform" does not mean there is no acceleration! Since the direction of the velocity changes constantly, there is indeed an acceleration (we will see this in chapter 2). Uniform only means that the magnitude of the velocity does not change.