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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.s1m.s^{-1} ] is given by:

v=2π×r60×Nv = \frac {2 \pi \times r}{60} \times N


Considering the units:

v(m.s1)=2π×r60×N(rpm)v_{(m.s^{-1})} = \frac {2 \pi \times r}{60} \times N_{(rpm)}

=602π×r×= \frac{60}{2\pi \times r} \times

v(m.s1)0.1047×r×N(rpm)v_{(m.s^{-1})} \approx 0.1047 \times r \times N_{(rpm)}

where:

  • vv is the linear velocity expressed in m.s1m.s^{-1}
  • NN i s the angular velocity expressed in rpmrpm
  • rr s the radius expressed in mm

Converting an angular speed to angular velocity

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:

  1. Determine the radius (r) of the circle: The radius should be in meters.

  2. Calculate the circumference (C) of the circle:

    C=2πrC = 2 \pi r

  3. Convert rpm to revolutions per second (rps):

    rps=rpm60\text{rps} = \frac{\text{rpm}}{60}

  4. Calculate the linear speed in meters per second (m/s):

    linear speed (m/s)=rps×C\text{linear speed (m/s)} = \text{rps} \times C

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

linear speed (m/s)=(rpm60)×(2πr)\text{linear speed (m/s)} = \left( \frac{\text{rpm}}{60} \right) \times (2 \pi r)

Example Calculation

Relationship between linear and angular velocity, example of a vehicle with 0.5m diameter wheels turning at 120 rpm.

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

  1. Calculate the circumference:

C=2π×0.5=π3.1416metersC = 2 \pi \times 0.5 = \pi \approx 3.1416 \, \text{meters}

  1. Convert rpm to rps:

rps=12060=2revolutions per second\text{rps} = \frac{120}{60} = 2 \, \text{revolutions per second}

  1. Calculate the linear speed:

linear speed=2×3.14166.2832m/s\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.