Question

Define angular displacement and angular velocity.

Answer 1

$\underline{\text{Angular displacement}}$ :- as we know, displacement is the the shortest distance between two points. similarly, angular displacement is the used to measure curve path. Thus, displacement of body moving in curved path is represented by angular displacement.It is defined as the angle in radians through which a point has been rotated about a specified axis.
For finding angular displacement we use the formula, θ = l/r , l = rθ here l is not other than angular displacement.

$\underline{\text{Angular velocity}}$ :- The Angular velocity is the measure of how fast a body is changing its angle. It is measured by radian per second.
Mathematically, $\bold{\omega=\frac{d\theta}{dt}}$
Here dθ represents change in angle and dt represents change in time.

Answer 2

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angular displacement

angular displacement in a given time of the object moving around a circular path is defined as the angle traced out by the radius vector at the centre of the circular path in the given time

angular displacement is a vector quantity provided theta is a small this is because the community relative law of vectors addition four three angles is not valid whereas for small angles the law is valid the direction of angular displacement depend upon the sense of rotation of the object and is given by right hand rule

angular velocity

angular velocity of an object in circular motion is defined as the time rate of change of its angular displacement it is generally denoted by Omega and is measured in Radian per second