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# Angular velocity and linear velocity

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

While I was watching the bags on the carousel, I've thought about the rate of speed they have. I've decided that it is easy to find; all you need to do is measure their revolutions per minute (n) and the carousel radius (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 are the angular velocity $\omega$. Linear velocity is trivial, 1 radian corresponds to arc with length of radius, thus
$v = \omega R$

#### Angular velocity and linear velocity

Digits after the decimal point: 2