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How to convert a linear velocity expressed in kilometres per hour [km/h] to an angular velocity expressed in revolutions per minute [rpm] ?
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The formula to convert a linear velocity expressed in kilometres per hour [km/h] to an angular velocity expressed in revolutions per minute [rpm] is given by:

N(rpm)=253.π.rv(km/h)N_{(rpm)} = \frac {25} { 3 .\pi . r} v_{(km/h)}

Where:

  • vv is the linear velocity expressed in kilometres per hour (km/h)
  • NN is the angular velocity expressed in revolution per minute (rpm)
  • rr is the radius expressed in meters (m)

Converting kilometers per hour (km/h) to revolutions per minute (rpm) requires knowing the circumference of the rotating object, such as a wheel or a shaft. Here’s how you can do it step-by-step:

Steps to Convert km/h to rpm:

  1. Determine the Circumference:

    • Measure or calculate the circumference CC of the rotating object in kilometers.

    • If you know the radius rr of the object, you can find the circumference using the formula:

      C=2π×rC = 2\pi \times r

      Ensure rr is in meters before converting to kilometers (divide by 1000).

  2. Convert km/h to m/s:

    • First, convert the speed from kilometers per hour to meters per second (m/s) using the conversion factor 10003600\frac{1000}{3600}:

      Speed in m/s=Speed in km/h×10003600\text{Speed in m/s} = \frac{\text{Speed in km/h} \times 1000}{3600}

  3. Calculate RPM:

    • Once you have the speed in meters per second and the circumference in kilometers, use the following formula to calculate rpm:

      RPM=Speed in m/s×60C\text{RPM} = \frac{\text{Speed in m/s} \times 60}{C}

      Where CC is the circumference of the rotating object in kilometers.

    • Replace CC by 2πr2\pi r :

      Nrpm=10003600×602π×r×v=253×π×rv(km/h)N_{rpm} = \frac{1000}{3600} \times \frac{60}{2\pi \times r} \times v = \frac {25} { 3 \times \pi \times r} v_{(km/h)}

Example Calculation:

Let's say you have a wheel with a radius of 0.35 meters (which gives a circumference C2.199C \approx 2.199 meters or 0.0021990.002199 kilometers) and it is moving at a speed of 50 km/h.

  1. Convert km/h to m/s:

    Speed in m/s=50×10003600=50000360013.89 m/s\text{Speed in m/s} = \frac{50 \times 1000}{3600} = \frac{50000}{3600} \approx 13.89 \text{ m/s}

  2. Calculate RPM:

    RPM=13.89×600.002199379 rpm\text{RPM} = \frac{13.89 \times 60}{0.002199} \approx 379 \text{ rpm}

Therefore, a wheel with a diameter of 0.35 meters (circumference approximately 2.199 meters or 0.002199 kilometers), moving at a speed of 50 km/h, would be rotating at approximately 379 revolutions per minute (rpm).


Here is an online unit converter that convert kilometers per hour [km/h] to revolutions per minute [rpm] and vice-versa.