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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.

### 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 $2\pi r \times N$.