Converting m/s to rad/s

Diagram of the conversion from omega linear speed to v linear speed

The formula for converting a linear velocity expressed in $m.s^{-1}$ into an angular velocity expressed in $rad.s^{-1}$ is given by :

$\omega = \frac{v}{r}$

With :

$\omega$ angular velocity expressed in $rad.s^{-1}$
$v$ linear velocity expressed in $m.s^{-1}$
$r$ radius, expressed in $m$

Example of converting angular velocity to linear velocity for vehicle wheels

For example, if a vehicle with wheels of radius 10 cm move at a speed of 2 m/s, the angular velocity of the wheels is given by :

$\omega = \frac{v}{r} = \frac{2 \text{ m/s}}{0.1 \text{ m}} = 20~ rad.s^{-1}$

You'll find on this page an online converter from linear to angular velocity.

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