Period and frequency

Beginner

Time for one revolution and revolutions per second.

Key relationT = 1/f = 2π/ω

The period T is the time for one revolution; frequency f = 1/T counts revolutions per second (hertz). ω = 2πf = 2π/T.

Worked example

A fan with f = 5 Hz has T = 0.2 s and ω = 31.4 rad/s.

Common mistake

rpm must be converted to Hz or rad/s before use.

In more detail

The period is the time for one full revolution, and the frequency is the number of revolutions per second. They are reciprocals: f = 1/T.

Power grids operate at 50 or 60 hertz, which is a frequency of alternating current.
Turntables and fan speeds are described by their rotation frequency.
A record player turns at 33 revolutions per minute, so its period is about 1.8 seconds per turn.

What is the unit of frequency?

Hertz, equal to one cycle per second.

How does angular frequency differ?

Angular frequency is 2π times the frequency, measured in radians per second.

How do I convert frequency to angular frequency?

Multiply by 2π, because one revolution is 2π radians.