CIRCULAR MOTION
1. Meaning of circular motion
 Definition of terms
 Angular velocity ii. Tangential velocity iii. Centripetal acceleration
 Centripetal force v. Centrifugal force vi. Period vii. Frequency
 Calculations on circular motion.
Meaning of circular motion
Circular motion is the motion of a body around a cicle. The simplest form of circular motion is the uniform circular motion, where the speed is constant but the direction is changing.
C 
V_{2} 
B 
A 
V_{1} 
Consider a body moving in a circular path center O with a constant speed.
 The direction at different points are not the same i.e the direction at A is different from the
direction at B. This leads to a change in velocity.
 This difference in velocity produces an acceleration directed towards the center of the
circle. This acceleration is called centripetal acceleration.
 Since there is an acceleration, there is a force directed towards the center of the circle
called centripetal force.
 In addition to the centripetal force, there is an equal and opposite force which acts
outwards from the center called the centrifugal force. These two forces enable the
object to move in the orbit.
Definition of terms used in circular motion.
 Angular velocity (ω): The ratio of the angle turned through to the elapsed time.
r r

ω = Angular velocity
ω =
The S.l unit is rad/sec
 Tangential velocity(V): This is the linear velocity in a tangential direction to the
circumference.
v = =
But, ω
Then v = rω
The unit is m/s
 Centripetal acceleration (a): It is the acceleration of a body moving in a uniform
circular motion and directed towards the center.
The unit is m/s^{2}
But , v = rω
Then, a = rω^{2}
 Centripetal force (F): It is defined as that inward force that is always directed towards the centre required to keep an object moving with a constant speed in a circular path.
Centripetal force = mass x centripetal acceleration
or F = rω^{2}= = ma
The unit is Newton
 Centrifugal force: This force is equal in magnitude to the centripetal force but opposite in
direction. (it is always directed away from the centre of the circle)
or F = – rω^{2}
 Period(T): This is the time taken for a body to complete one revolution round the circle.
Displacement = 2
Time = T
Velocity = v
v =
T
 Frequency (f): It is the number of revolutions in one second.
f
T
The unit is Hertz or per seconds. (Ie Hz or s^{1})
Calculations on circular motion
Question 1: A stone of mass 2kg is attached to the end of an inelastic string and whirled round two times in a horizontal circular path of radius 3m in 3 sec, find:
 Angular velocity
 Linear velocity
iii. Centripetal acceleration
 Centripetal force
 Centrifugal force
SOLUTION
 ω=
Where is the angular displacement and ω is the angular velocity
θ = 360 X 2 = 720^{}(ie two times)
π = 180^{}
θ = 4π rad
ω= = 1.33πrad/sec
 v = rω
= 3 x 1.33π = 3.99 π m/s
m/s^{2}
^{ }
GENERAL EVALUATION
 Explain the following terms (i) Angular velocity (ii) Tangential velocity
(iii) centripetal acceleration
 A body of mass 10kg is attached to the end of an inelastic thread and whirled round in a
circular path of radius 0.3m, if the body makes a complete revolution in 3 sec find
 Angular velocity
 linear velocity
 centripetal acceleration
 centripetal force
 centrifugal force