CIRCULAR MOTION

Direction : Infinitesimal angular displacement, angular velocity and angular accel-eration are vector quantities whose direction is given by right hand rule.

Right hand Rule : Imagine the axis of rotation to be held in the right handwith fingers curled round the axis and the thumb stretched along the axis.If the curled fingers denote the sense of rotation, then the thumb denoted thedirection of the angular velocity (or angular acceleration of infinitesimal angulardisplacement .

1.4 Angular acceleration (a) The rate of change of angular velocity with time is called angular acceleration.

Average angular acceleration

2 1

2 1t t t

= =

Instantaneous angular acceleration

2

2d ddt dt

= =

It is a vector quantity, whose direction is along the change in direction of angular velocity.

S.I. Unit : radian/sec2

Dimension : M0L0T2

1.5 Relation between angular velocity and linear velocity

Suppose the particle moves along a circular path from point A to point B in infinitesimally small time t.

As, t 0, 0

arc AB = chord AB i.e. displacement of the particle is along a straight line.

Linear velocity, v = t 0

slimt

But, s = r.

v = t 0

r. slim rt

=

t 0lim

t

But, t 0lim

t = = angular velocity

v = r . [For circular motion only]i.e. (linear velocity) = (Radian) (angular velocity)

In vector notation, v r

= [in general]

Linear velocity of a particle performing circular motion is the vector product of its angular velocity andradius vector.

O

B

Ar

s

downward

clockwise

upward

Anti-clockwise