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Special Case : Circular Motion

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)

= v2 / r = w2r2 /r  =w2 r

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

v = v0 +atà Linear velocity equation

w = w0 +atà Angular velocity equation.

 

Linear

v

s

vo

so

Angular                    Linear                         Angular

W                              a                                    ex

e

W                              0

θ                                0