Question

A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?

Answer 1

Hint: We know that revolution per minute, denoted by rpm, represents the number of turns in one minute. It represents the frequency of rotation of an object around a fixed axis. We can change the revolution per minute into radian per second by multiplying it by \[\left( \dfrac{2\pi }{60} \right)\].

Complete step-by-step answer:
We have been given that a wheel makes 360 revolutions per minute.
We know that revolution per minute is a rotation unit of speed. A revolution is equal to 1 rotation around a circle, i.e. \[2\pi \] radians angle subtended at the center and 1 minute is equal to 60 seconds. So to convert the revolution per minute into radians per second, we will multiply it by \[\left( \dfrac{2\pi }{60} \right)\].
\[\Rightarrow \] In radian speed \[=360\times \dfrac{2\pi }{60}\] radian/ sec \[=6\times 2\pi \] radian/ sec \[=12\pi \] radian/ sec
Therefore, the wheel turns by \[=12\pi \] radians in 1 second.

Note: Remember that revolution per minute is abbreviated as rpm, RM, rev/ min is the number of turns in one minute. Also, rpm is not a unit according to the International System of Units. Also, remember that there is a difference between radius and radian. Radius is the distance from the center of a circle to its perimeter but a radian is an angle whose corresponding arc in a circle is equal to the radius of the circle.