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.
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‘.
“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.
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.