Circular Motion-Angular Motion-Radian

Uniform circular motion
When an object moves in a circular path such that the magnitude of velocity is constant then, the motion is called uniform circular motion.

Angular motion
When a body moves along a circular path it traverses a certain angle in a given interval of time. This type of motion is called ‘angular motion‘.

Angular displacement
“The angle traveled by a body during its motion around
a circular path is called its angular displacement.”
Consider a particle moves in a circular path from a point P1 to P2 in an interval of time Dt. It travels an angle <p1OP2 = q which is called angular displacement of the particle.

Radian
One radian is the angle traced by an arc of length equal to radius of circle.
Length of circular track of radius r is 2p r. Therefore, numbers of radians in a circle of radius r will be
=2p r / r
= 2pAngle at the centre of circle in one complete rotation = 360o = 2p rad
180o = p rad or 1o = p / 180 rad.

Relation between length of arc and the angle subtended
The length of arc “S” is directly proportional to angle q subtended (measured in radians) traced at the centre of circle by ends of the arc.
S a q
S = rq
Where r is radius of circle.