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How to convert revolutions per minute [rpm] to meters per second [m/s]

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

$v = \frac {2 \pi \times r}{60} \times N$

Considering the units:

$v_{(m.s^{-1})} = \frac {2 \pi \times r}{60} \times N_{(rpm)}$

$= \frac{60}{2\pi \times r} \times$

$v_{(m.s^{-1})} \approx 0.1047 \times r \times N_{(rpm)}$

where:

- $v$ is the linear velocity expressed in $m.s^{-1}$
- $N$ i s the angular velocity expressed in $rpm$
- $r$ s the radius expressed in $m$

To convert revolutions per minute (rpm) to meters per second (m/s), you need to know the circumference of the circle that the rotating object is tracing out. Here's a step-by-step guide on how to do the conversion:

**Determine the radius (r) of the circle**: The radius should be in meters.**Calculate the circumference (C) of the circle**:$C = 2 \pi r$

**Convert rpm to revolutions per second (rps)**:$\text{rps} = \frac{\text{rpm}}{60}$

**Calculate the linear speed in meters per second (m/s)**:$\text{linear speed (m/s)} = \text{rps} \times C$

Putting it all together, the formula to convert rpm to m/s is:

$\text{linear speed (m/s)} = \left( \frac{\text{rpm}}{60} \right) \times (2 \pi r)$

Let's take the example of a vehicle with 0.5m diameter wheels turning at 120 rpm.

- Calculate the circumference:

$C = 2 \pi \times 0.5 = \pi \approx 3.1416 \, \text{meters}$

- Convert rpm to rps:

$\text{rps} = \frac{120}{60} = 2 \, \text{revolutions per second}$

- Calculate the linear speed:

$\text{linear speed} = 2 \times 3.1416 \approx 6.2832 \, \text{m/s}$

So, a wheel with a radius of 0.5 meters rotating at 120 rpm has a linear speed of approximately 6.2832 meters per second.