Question

How do you convert $rev/s$ to $rad/\sec $?

Answer 1

Hint: We have to remember that one revolution takes a complete circle. That is, one revolution takes an angle of $2\pi radians$ or $360^\circ $.

Formula used: $1rev = 2\pi rad$.

Complete step-by-step answer:
We know that $1rev = 2\pi rad$.
Here we are assigned units of angular velocity in the question.
$1rev/s$ implies that it takes $1\sec $to complete $1rev$.
$ \Rightarrow $ it takes $1\sec $to complete $2\pi rad$.
$ \Rightarrow 1rev/s = 2\pi rad/\sec $ , which is our required relation.
Approximating $\pi \approx 3.14$, we can also write the relation as follows:
$1rev/s = 2\pi rad/\sec $
$ = 2 \times 3.14rad/\sec $
 $ = 6.28rad/\sec $
That is,
$1rev/s = 2\pi rad/\sec = 6.28rad/\sec $ $$.

Additional information:
The time taken by an object to make a complete circular path is called a period. Completion of one revolution takes one period.
The units $rev/s$ and $rad/\sec $ are mostly used in physics and engineering.
They are especially used in mechanics in the calculation of the power transmitted by a shaft.
These are also used in expressing the average angular velocity of planets around their stars. For example, the angular velocity of earth is approximately equal to $2.0 \times {10^7}rad/s$.
Formally used unit of angular velocity instead of $rev/s$is $rev/\min $.

Note: The formal definition of radian per second is as follows:
1. “Is the change in orientation of an object, in radians, every second”.
2. While revolution per second is “the number of turns in one second”.