Period and Frequency in Circular Motion
Simple Explanation
For an object moving at constant speed around a circle, the period (T) is the time for one complete revolution, and the frequency (f) is how many revolutions happen per second β frequency is simply the reciprocal of the period.
Why Do We Need It?
Period and frequency describe the basic "rhythm" of circular motion and are the starting point for calculating centripetal acceleration and force.
Formula
Period, Frequency and Speed in Circular Motion
T = 2Οr / v, f = 1/T
Relates how long one full revolution takes (period) to the radius and speed of circular motion, and how frequency is the reciprocal of period.
- T
- β Period β time for one complete revolution, in seconds
- r
- β Radius of the circular path, in metres
- v
- β Constant speed along the circular path, in m/s
- f
- β Frequency β number of revolutions per second, in Hz
When to use it: Use to relate the speed, radius, period, and frequency of any object moving at constant speed in a circle.
Worked Example
Finding period and speed
A stone on a 0.5 m string is whirled in a circle, completing one revolution every 0.4 s. Find its speed and frequency.
Why Does This Work?
In one period, the object travels exactly the circumference of the circle (2Οr) β dividing this distance by the period gives its constant speed, matching the ordinary distance/time relationship applied to a circular path.
Real-Life Example
A spinning fan blade tip
A ceiling fan's blade tip moves in a circle as the fan rotates.
The fan's rotational speed (revolutions per minute) is directly related to the frequency of the blade tip's circular motion β converting RPM to frequency (Hz) and using the blade length as the radius lets you calculate the actual speed of the blade tip.
Practice
An object completes 5 revolutions in 2 seconds. Find its frequency.
EasyCommon mistake
Confusing period and frequency β period (T) is measured in seconds (time per revolution); frequency (f) is measured in Hz (revolutions per second). They are reciprocals of each other, not the same thing.
Quick Review
- Period T: time for one full revolution. Frequency f = 1/T.
- Speed v = 2Οr/T = circumference Γ· period.
- These quantities describe circular motion before centripetal acceleration is calculated.