In converting revolutions per minute to radians per second, which constant is used?

When converting revolutions per minute (RPM) to radians per second, it is essential to understand the relationship between revolutions and radians. One complete revolution corresponds to (2\pi) radians. Therefore, to convert from revolutions to radians, you multiply the number of revolutions by (2\pi).

Additionally, since the conversion is from a measurement per minute (RPM) to a measurement per second (radians per second), you divide by 60 to account for the minute to second conversion. Thus, the formula for the conversion is:

[ \text{Radians per second} = \text{RPM} \times 2\pi \text{ (radians per revolution)} \times \frac{1}{60} \text{ (minutes to seconds)}. ]

Using (2\pi) is crucial because it allows for the conversion from the unit of revolutions, which is circular in nature, to the angular measurement of radians, which is a more fundamental unit in trigonometry and physics for angular measurements. This illustrates that multiplying by (2\pi) effectively captures the complete circular movement represented by each revolution.