How to Find Revolutions Per Minute Given Radius and Speed

To find the revolutions per minute (RPM) given the radius and linear speed, you can use the following formula:

RPM = (Speed in units per minute) / (2 × π × Radius)

Here’s how it works:

1. Convert the speed: Ensure that the speed is in the same units per minute as the radius, or convert it appropriately. For example, if the radius is in meters and the speed is in meters per second, first convert the speed to meters per minute by multiplying by 60.
2. Calculate the circumference: The circumference of the circle is calculated using the formula C = 2 × π × Radius. This gives you the distance traveled in one complete revolution.
3. Determine RPM: Divide the linear speed by the circumference to find how many revolutions occur in one minute.

Let’s take an example: If the radius is 0.5 meters and the speed is 3 meters per second:

1. First, convert the speed:
   3 meters/second × 60 seconds/minute = 180 meters/minute.
2. Next, calculate the circumference:
   C = 2 × π × 0.5 ≈ 3.14 meters.
3. Now compute the RPM:
   RPM = 180 / 3.14 ≈ 57.3 revolutions per minute.

Therefore, if you have the radius and the linear speed, you can easily calculate the RPM using this method!