Question

The unit of angular acceleration in the $SI$ system is
(A) $N\,K{h^{ - 1}}$
(B) $m{s^{ - 2}}$
(C) $rad{s^{ - 2}}$
(D) $mK{g^{ - 1}}K$

Answer 1

Hint If the motion takes place in a circular or a semicircular way, then the motion, velocity and the acceleration all are specified by the angular acceleration. The $SI$ unit is the standard system of units that is used mostly all over the world.

Useful formula
(1) The formula of the angular acceleration is given by
$\alpha = \dfrac{\omega }{t}$
Where $\alpha$ is the angular acceleration, $\omega$ is the angular velocity and the $t$ is the time taken for the angular movement.
(2) The formula of the angular velocity is given by
$\omega = \dfrac{\theta }{t}$
Where $\theta$ is the angular displacement.

Complete step by step solution
The angular acceleration is defined as the rate of change of the angular velocity with that of the time. Or it can also be defined as the twice the rate of change of the angular displacement with that of the time.
Using the formula of the angular acceleration,
$\alpha = \dfrac{\omega }{t}$
Substituting the formula (2) in the formula (1) , we get
$\alpha = \dfrac{{\dfrac{\theta }{t}}}{t}$
By simplification of the above equation, we get
$\alpha = \dfrac{\theta }{{{t^2}}}$
The $SI$ unit of the angular displacement is radians and the $SI$ unit of the time taken is second. Substituting these in the above formula, the $SI$ unit of the angular acceleration is obtained as $rad{s^{ - 2}}$ .

Thus the option (C) is correct.

Note Remember that the $SI$ unit of the length is metre, mass is kilogram, time is second, angular length is radian, and the temperature is kelvin. They are the fundamental quantity. The angular acceleration is the derived quantity that is obtained from the above fundamental quantities.