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.

Explanation:

• 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 $2\pi r \times N$.