CIRCULAR MOTION

CIRCULAR MOTION

 

1. Meaning of circular motion

  1. Definition of terms
  2. Angular velocity ii. Tangential velocity iii. Centripetal acceleration
  3. Centripetal force v.  Centrifugal force  vi.  Period  vii. Frequency
  4. 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
V2
B
A
V1

 

Consider a body moving in a circular path center O with a constant speed.

  1. 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.

  1. This difference in velocity produces an acceleration directed towards the center of the

circle. This acceleration is called centripetal acceleration.

  1. Since there is an acceleration, there is a force directed towards the center of the circle

called centripetal force.

  1. 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.

 

  1. 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

 

  1. 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

  1. 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/s2

 

But ,  v = rω

 

Then,  a = rω2

 

  1. 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 =2=  = ma

 

The unit is Newton

 

  1. 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 =  –2

 

  1. 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

 

 

  1. 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:

  1. Angular velocity
  2. Linear velocity

iii.  Centripetal acceleration

  1. Centripetal force
  2. Centrifugal force

 

SOLUTION

 

  1. ω=

Where  is the angular displacement and ω is the angular velocity

 

            θ = 360 X 2 = 7200(ie two times)

π = 1800

θ = 4π rad

ω=  = 1.33πrad/sec

 

  1. v = rω

= 3 x 1.33π = 3.99 π m/s

 

 

 

m/s2

 

 

 

 

GENERAL EVALUATION

 

  1. Explain the following terms (i)  Angular velocity  (ii)  Tangential velocity

(iii) centripetal acceleration

  1. 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

  1. Angular velocity
  2. linear velocity
  3. centripetal acceleration
  4. centripetal force
  5. centrifugal force

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