Revolutions per minute describes the angular velocity of a rotational device, such as an engine or a Ferris wheel at an amusement park. In mathematical terms, the radian measure is equal to the length of the arc that subtends or "stretches under" an angle, theta, on a circle of radius 1. One revolution around a circle is 2 pi radians, and pi is approximately 3.14. To convert rpm to radians, calculate the equivalent radians per second and then get the radians over a specific time interval.
Convert rpm to radians per minute. A revolution is one turn around a circle, which is 2 pi radians. Therefore, 1 rpm equals 2 pi radians per minute. For example, 10 rpm equals 20 pi radians per minute (10 x 2 pi). Multiply 20 pi by 3.14 to calculate 62.8 radians per minute.
Convert rpm to radians per second. Because a minute has 60 seconds, 1 rpm equals 1/60 revolution per second. Therefore, 1 rpm equals pi/30 radians per second (2 pi / 60). For example, if you're converting 10 rpm to radians per second, multiply 10 by pi/30 to calculate 0.33 pi radians per second, or about 1.05 radians per second.
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Calculate the radians over any given time interval. For example, suppose an engine’s speed rating is 60 rpm and you want to know the radians traveled in 10 seconds. So multiply 60 by pi/30 by 10 to calculate the distance the motor turns. That's about 62.8 radians (20 pi x 3.14).