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How to convert metres per second to rad per second?

alphonsio

The formula to convert **linear speed** $v$ expressed in meters per second [ $m.s^{-1}$ ] to to **angular velocity** $\omega$ expressed in radians per second [ $rad.s^{-1}$ ] is given by:

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

$\omega_{(rad/s)}=\dfrac{v_{(m/s)}}{r_{(m)}}$

where:

- $v$ is the linear velocity expressed in meters per second ( $m.s^{-1}$ )
- $\omega$ is the angular velocity expressed in radians per second ( $rad.s^{-1}$ )
- $r$ is the radius expressed in meters ( $m$ )

Here is an online converter from m/s to rad/s.

You need to know the radius of the circular path along which the object is moving. This is because the relationship between linear velocity (in m/s) and angular velocity (in rad/s) depends on the radius.

Here's how you can use this formula:

**Determine the linear velocity (v)**in meters per second.**Determine the radius (r)**of the circular path in meters.**Divide the linear velocity by the radius**to get the angular velocity.

Let's say an object is moving at a linear velocity of $2 \, \text{m/s}$ along a circular path with a radius of $0.1 \, \text{m}$ (=10cm).

Using the formula:

$\omega = \frac{2 \, \text{m/s}}{0.1 \, \text{m}} = 20 \, \text{rad/s}$

So, the angular velocity would be $20 \, \text{rad/s}$.

If you have specific values for the linear velocity and the radius, you can plug them into the formula to get the angular velocity.