Angular Motion

The motion of an object about a fixed point or fixed axis, as of planet or pendulum is called angular motion. Different volumes in rotational motion are analogous to the corresponding quantities in translational motion (simplest form of a motion that is the motion along a straight line). Angular displacement is similar to linear displacement, angular velocity to linear velocity, angular acceleration to linear acceleration, torque to force and mass to the moment of inertia. Angular motion is measured in terms of degrees per second (or hour) … or radians per minute, or arc seconds per year, or … i.e. an angle per a unit of time.

Consider a particle performing an angular motion about a fixed line in an anticlockwise direction. 

Then,

Angular Displacement:

Suppose that particle moves from point Q to the point P along x-axis in time t. During this time, the radius vector (a vector drawn from the center of the circle to the position of the particle) rotates through an angle ∠QOP = θ.This angle is called as angular displacement of the particle in time t. Thus, angular displacement of the particle in a given time is equal to the angle traced by its radius vector in that time. It is measured in radians. Angular displacement possesses magnitude as well as direction. Hence it can be regarded as vector quantity.  

Angular displacement = Angle in Radian = Arc / Radius

Angular velocity:

The rate of change of angular displacement with time is called angular velocity (v) of the particle or angular velocity is the angle traced per unit time by the radius vector. The SI unit of angular velocity is radian per second(rad/s). It is the vector quantity and its direction can be represented by right hand rule. From fig.,

Angular velocity = Angular Displacement /Time

v = θ / t

Angular Acceleration(α):

The rate of change of angular velocity is called the angular acceleration

Angular Acceleration(α) = Change in Angular Velocity / Time

Torque:

A torque applied to a particle produces angular acceleration

Torque=moment of inertia × angular acceleration

T=I α