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:

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

Example

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.