Here r = constant

Scalar components of velocity and acceleration

v =r θ

an = v2 /r = r θ ^{2 }= v θ

at = dv /dt = v = rθ

e is measured from any convenient radial reference to OP.

**2.6.1 Angular Velocity**

It is defined as the rate of change of angular displacement of a particle

w =angular velocity =dθ / dt =θ

equation (2.21) => v rθ = rw

liner velocity = r x angular velocity

unit of w = rad /s w =rad / s

**2.6.2 Angular Acceleration**

It is defined as the rate of change of angular velocity

a = dw /dt= d2θ /dt2 =θ =w

at( tangential acceleration) = dv / dt = v = rθ

= r w = r dw /dt

= ra

an (normal acceleration)

= v^{2} / r = w^{2}r^{2} /r =w_{2} r

For angular velocity, all the equations derived for linear velocity will be applicable. For example,

v = v_{0} +atà Linear velocity equation

w = w_{0} +atà Angular velocity equation.

Linear
v s vo so |
Angular Linear Angular
W a ex e W 0 θ 0 |