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
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