Question

The angular velocity ( in $rad/s$ ) of a body rotating at $N$ rpm is
$A.\dfrac{\pi N}{60}$
$B.\dfrac{2\pi N}{60}$
$C.\dfrac{\pi N}{120}$
$D.\dfrac{\pi N}{180}$

Answer 1

We will use the relationship of angular velocity and revolution per minute (rpm). Angular velocity is defined as the angular displacement per unit time. Revolution made in one minute is termed as the revolution per minute.
Formula Used:
We are going to use the following formula to solve the problem:-
$\omega =\dfrac{2\pi }{T}$

Complete answer:
Suppose a body is rotating with angular velocity, $\omega$in time $T$ seconds then its angular velocity is given as follows:-
$\omega =\dfrac{2\pi }{T}$ …………. $(i)$
We have to find in revolution per minute and we know that $1\min =60s$, then equation $(i)$ becomes
$\omega =\dfrac{2\pi }{60}$ …………….. $(ii)$
For $N$ number of revolutions this equation $(ii)$ becomes
$\omega =\dfrac{2\pi N}{60}rad/s$

Hence, option $(B)$ is correct.

Additional Information:
Angular velocity is defined as the angular displacement per unit time. It is generally represented with the help of a Greek letter which is known as omega ( $\Omega$ ). It tells how fast the angular position of an object changes with respect to time. The SI unit of angular velocity is radians per second. By convention, positive angular velocity is indicated with anti-clockwise rotation while negative angular velocity is indicated with clockwise rotation. If the angles are measured in radians then linear velocity is the product of angular velocity and the radius. Revolution per minute is the number of turns in one minute. It is also used to represent the angular speed.

Note:
We should give our attention towards the fact that radians per second and revolution per minute are different units to represent angular velocity or speed. Conversion of minutes into seconds or vice versa should also be taken care of. Correct use of relations should be applied.