You can calculate the revolutions per minute (rpm) of a circular object if you know its radius and how far it travels in a straight line in a given period of time. You may need to do some unit converting, for instance between miles per hour (mph) and feet per second, but otherwise, the calculation is fairly simple.
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Things you need
Measure or identify how fast a circular object rotates in linear speed.
For example, if a car drives forward with a speed of 50mph, then a given point on the edge of one of the four tires has a speed of 50mph relative to the centre of the wheel also.
Measure or identify the radius, r, or diameter, d, of the circular object. The radius is the distance from the centre of a circle to its edge. The diameter is the distance from one point on a circle to the point on the opposite side. Therefore, the diameter is twice the radius.
For example, a car's tire may have a diameter, d, of 30 inches, or a radius, r, of 15 inches.
Find the circumference from the measurement in Step 2 by multiplying the diameter times a constant called "pi", which is the ratio for all circles between the circumference and diameter. Pi equals 3.14159 (after rounding to the fifth decimal place).
Continuing with the above example, the diameter of 30 inches multiplied by the ratio of pi, 3.14159, equals 94.25 inches.
Convert the original rate to the circular object's unit of measurement.
Continuing with the above example, 50 MPH can be multiplied by 63,360 inches / mile and then multiplied by 1 hour / 3,600 seconds to get 880 inches / second. Converting to a small time unit helps make the inches measurement more manageable.
Divide the rate of speed by the circumference to get the number of revolutions per unit of time.
Continuing with the above example, a tire with a circumference of 94.25 inches travelling at 880 inches/second is turning at 9.34 revolutions per second. In other words, you divide 880 by 94.25 to get 9.34.
Tips and warnings
- One way of accurately measuring circumference is to roll the circular object through ten revolutions, see how far it went, and divide by 10.
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