Question

define angular displacement angular velocity and angular acceleration

Answer 1

Angular displacement of a body is the anglein radians (degrees, revolutions) through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis. When an object rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of an object, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the objects motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible. Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion.

Angular Velocity is a measure of how quickly an object moves through an angle. It is the change in angle of a moving object (measured in radians), divided by time. Angular velocity has a magnitude (a value) and a direction.
Angular acceleration is the rate of change of angular velocity. In three dimensions, it is a pseudovector. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha(α).[1]

Answer 2

⭕ Angular Displacement => It is the angle subtended by the position vector at the centre of the circular path.

Angular displacement (∆θ) = (∆S/r)

where ∆S is the linear displacement and r is the radius . It's unit is radian.

⭕ Angular Velocity => The time rate of change of angular displacement (∆θ) is called Angular Velocity.

Angular Velocity (ω) = (∆θ / ∆t)

It is vector quantity and it's S.I. unit is rad/s.

⭕ Angular Acceleration => The time rate of change of angular Velocity is called Angular Acceleration.