CIRCULAR MOTION

2.2 Non uniform circular motion

A circular motion in which both the direction and magnitude of the velocity changes is called nonuniformcircular motion.

A merry-go-round spinning up from rest to full speed, or a ball whirling around in a vertical circle.

The acceleration is neither parallel nor perpendicular to the velocity.

We can resolve the acceleration vector into two components :

Radial Acceleration : ar perpendicular to the velocity changes only the directions of velocity Acts

just like the acceleration in uniform circular motion.

ac = or

2

r

va

r=

Centripetal force : Fc =

22mv m r

r=

Tagential acceleration : ar parallel to the velocity (since it is tangent to the path)

changes magnitude of the velocity acts just like one-dimensional acceleration

at = dvdt

Tangential acceleration : at = dvdt , where v =

dsdt and s = length of arc

Tangential force : Ft = matThe net acceleration vector is obtained by vector addition of these two components.

2 2r ta a a= +

(a) In non-uniform circular motion :

speed | v | constant angular velocity constant

i.e. speed constant i.e. angular velocity constant

(b) In at any instant v = magnitude of velocity of particle r = radius of circular path

= angular velocity of a particle

then, at that instant v = r

Net force on the particle

+= tc FFF 2t

2c FFF +=

If is the angle made by F = Fc,

then tan = tc

FF = tan

1

t

c

FF

[Note angle between Fc and Ft is 90]

Angle between F and Ft is (90 )

F

FCFt

FC