How to find velocity of a rotating object from frequency?
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◆ ∆nswer ◆
Simple :. we know , v = w × r
where ,
v = velocity
w = angular velocity
r = radius of rotation..
now , f = frequency = 1/ Time period = w/2π
as , w = 2π/T
so , v = 2πfr
#Superman
Simple :. we know , v = w × r
where ,
v = velocity
w = angular velocity
r = radius of rotation..
now , f = frequency = 1/ Time period = w/2π
as , w = 2π/T
so , v = 2πfr
#Superman
Answered by
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There are many ways to find the frequency in uniform circular motion 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, ω , but they are related through this:
2π⋅f=ω
We also know that the period, T, is related to f through T=1f
If the speed is known then you can use:
v=2πrT=2πrf ⇒f=v2πr
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=20s5=4s
The frequency is then f=1T=14s=.25s=.25s−1=.25Hz
The angular freq is then ω=2π⋅0.25Hz=1.57rads
First, be clear that there is a difference between the "frequency", f, and the angular frequency, ω , but they are related through this:
2π⋅f=ω
We also know that the period, T, is related to f through T=1f
If the speed is known then you can use:
v=2πrT=2πrf ⇒f=v2πr
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=20s5=4s
The frequency is then f=1T=14s=.25s=.25s−1=.25Hz
The angular freq is then ω=2π⋅0.25Hz=1.57rads
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