user

What is the formula to convert angular velocity in revolution per second to linear velocity in meters per second?

alphonsio

The formula to convert **angular velocity** expressed in revolutions per seconde [ $rps$ ] to **linear speed** expressed in meters per second [ $m.s^{-1}$ ] is given by:

$v = 2\pi r \cdot N$

$v_{(m.s^{-1})} = 2 \pi \times r \times N_{(rps)}$

$v_{(m.s^{-1})} \approx 6.2831853. r .N_{(rps)}$

where:

- $v$ is the linear velocity expressed in meters per second ( $m.s^{-1}$ )
- $N$ is the angular velocity expressed in revolution per second ( $rps$ )
- $r$ is the radius expressed in meters ( $m$ )

To convert angular velocity in revolutions per second (rev/s) to linear velocity in meters per second (m/s), you can use the following formula:

$v = 2\pi r \cdot N$

where:

- $v$ is the linear velocity in meters per second (m/s).
- $r$ is the radius of the circular path in meters (m).
- $N$ is the angular velocity in revolutions per second (rev/s).
- $2\pi r$ represents the circumference of the circle.

- The circumference of a circle is $2\pi r$.
- If an object completes one revolution, it travels a distance equal to the circumference.
- Therefore, if it completes $N$ revolutions in one second, the linear velocity $v$ is given by the distance traveled per second, which is $2\pi r \times N$.