Question

The angular displacement is
A. a scalar
B. a vector
C. neither ( a ) nor ( b ).
D. either ( a ) or ( b )

Answer 1

Hint: Angular displacement occurs only when curvilinear motion is exhibited. The term angular depicts an angle and the term curvilinear means a curve that can never be depicted without an angle. So in this question to understand what is angular displacement we need to know the concept and how it takes place, what are its units and how it is represented mathematically then only we can find the answer.

Formulas used:
$\theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}}$

Complete step by step answer:
To understand what is angular displacement we at first need to know the definition of angular displacement and what is the concept behind it?
Angular displacement is actually the shortest angle between the final and initial position for a given object that is having a circular motion about a fixed point. Angular displacement here is a vector quantity.
So we know that vectors have directions as well as magnitude. We can represent the direction of angular displacement by a circular arrow which is pointing from the initial to the final position. The arrow may be in an anticlockwise or clockwise direction.
We can represent angular displacement mathematically as,
$\theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}}$
Now, actually the object that is moving and exhibiting angular displacement is actually moving in a fixed axis so we can say that the vector which is denoting angular displacement is an axis vector.
Angular displacement has units as Degree or radians.
Angular displacement is not completely considered as a vector quantity as while calculating the angular displacement it does not follow the law of vector addition. But in some cases like infinitesimal small angles, it follows vectors law of addition.
Based on the above explanation we can say that option D is the correct option.

Note:
In the equation $\theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}}$,$\theta $ is the angular displacement of the object, $\alpha $ is the angular acceleration , t is the time, $\omega $ is the initial angular velocity, r is the radius of curvature. And if we want to represent distance we use ‘s’. So to solve this question one must remember the mathematical form of the angular displacement as well the definition and concept behind it.