How do you find frequency in uniform circular motion?

There are many ways to find the frequency in uniform depending on what is given to you in the problem.

First, be clear that there is a difference between the "frequency", f, and the angular frequency, ##omega## , but they are related through this: ##2pi*f=omega##

We also know that the period, T, is related to f through ##T=1/f##

If the speed is known then you can use: ##v=(2πr)/T=2πrf## ##⇒f=v/(2πr)## This equation comes from knowing the distance travelled for one complete revolution is ##2πr## and the time taken is ##T##.

Example problem: If a ball takes 20 seconds to make 5 full revolutions, find its period, frequency, and angular frequency.

The period is the time it take for ONE revolution, so ##T=(20s)/5 = 4s##

The frequency is then ##f=1/T=1/4s=.25/s=.25s^-1##=.25Hz

The angular freq is then ##omega = 2pi*0.25Hz=1.57(rad)/s##