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Angular velocity and linear velocity

This online calculator converts angular velocity to linear velocity for given radius

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While I was watching kids on carousel I've thought about which speed did they have. I've decided that it is easy to find, all you need to do is just measure their revolutions per minute (n) and radius of carousel (R).

With revolutions per minute one can find angular speed - one revolution changes the angle by 2\pi radians, thus per minute it is 2\pi n radians, and per second it is \frac{2\pi n}{60} radians.

Radians per second is the angular velocity \omega. Linear velocity is trivial, 1 radian corresponds to arc with length of radius, thus
v = \omega R

PLANETCALC, Angular velocity and linear velocity

Angular velocity and linear velocity

Digits after the decimal point: 2
Angular velocity (radians per second)
 
Linear velocity (kms per hour)
 

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