Question

SI unit of the angular velocity is
(A). $m/s$
(B). $rad$
(C). $rad/s$
(D). $m/rad$.

Answer 1

Hint: You can start by briefly explaining angular velocity. Then write its equation, i.e. $\omega ={\displaystyle \frac{\theta }{t}}$ . Then use the SI unit of $\theta$ (measured in $rad$ ) and $t$ (measured in $\sec$ ) to calculate the SI unit of angular velocity. You can also mention some other units of angular velocity for extra information.

Complete step-by-step answer:
Angular velocity – Angular velocity describes how fast an object rotates or revolves in comparison to a reference point.
Or
It can also be defined as the rate of change of angular displacement (the change in angular displacement per unit time)
The symbol for angular velocity is $\omega$ .
We also know that the symbol for angular displacement and time is $\theta$ and $t$ respectively.
So, $\omega ={\displaystyle \frac{\theta }{t}}$
The SI unit of angular displacement is $rad$ and the SI unit of time is $\sec$ .
So, the SI unit of angular velocity becomes $rad/\sec$ which can also be written as $rad/s$ .
There are various other units for angular velocity like degrees per second, degrees per hour, and rotations per unit time or revolutions per minute (commonly called rpm).
It is very important to remember that changing the unit does not change the angular velocity, units are just different standards against which a quantity is compared. If you are confused in when to use a unit and when to not use it, remember it largely depends on the situation and the criteria given in the problem
Hence, option C is the correct choice.

Note: Angular velocity is a pseudovector, meaning it can behave both as a scalar and vector quantity. It behaves as a scalar when only the magnitude is mentioned, for example – A wheel is moving with an angular velocity of $10rad/s$ and behaves like a vector when the direction is given, for example - A wheel is moving with a velocity of $10rad/s$ in the clockwise direction.