Period, Frequency and Revolution
Simple Explanation
The period (T) is the time for one complete revolution; the frequency (f) is how many revolutions happen per second. They are reciprocals of each other, and both connect directly to angular velocity: Ο=2Οf=2Ο/T.
Why Do We Need It?
Period and frequency are the everyday, easy-to-measure way to describe a rotation's speed β "how many times per second" or "how many seconds per turn" β that connects directly to the more abstract angular velocity.
Formula
Period, Frequency and Angular Velocity
T = 1 / f; Ο = 2Οf = 2Ο / T
Connects how long one full revolution takes (period), how many revolutions happen per second (frequency), and the angular velocity of the rotation.
- T
- β period β time for one full revolution, in seconds (s)
- f
- β frequency β revolutions per second, in hertz (Hz)
- Ο
- β angular velocity, in radians per second (rad/s)
When to use it: Whenever converting between how often something rotates (frequency), how long one rotation takes (period), and its angular velocity.
Worked Example
Find period and angular velocity from frequency
A fan rotates at a frequency of 5 revolutions per second. Find its period and angular velocity.
Why Does This Work?
One full revolution sweeps through exactly 2Ο radians. If f revolutions happen every second, then 2Οf radians are swept every second β which is exactly the definition of angular velocity, Ο=2Οf.
Real-Life Example
A ceiling fan's rotation speed
A ceiling fan's speed setting is described by how many revolutions it completes per minute or second.
That frequency directly determines both the time for one blade rotation (its period) and its angular velocity, via T=1/f and Ο=2Οf.
Practice
A wheel has a period of 0.1 s. Find its frequency.
EasyCommon mistake
Mixing up period and frequency β a LARGER frequency (more revolutions per second) means a SMALLER period (less time per revolution), since T=1/f.
Quick Review
- T = 1/f β period and frequency are reciprocals.
- Ο = 2Οf = 2Ο/T connects both to angular velocity.
- Frequency is measured in hertz (Hz); period is measured in seconds (s).