## CIRCULAR MOTION

1. Meaning of circular motion

- Definition of terms
- Angular velocity ii. Tangential velocity iii. Centripetal acceleration
- Centripetal force v.Â Centrifugal forceÂ vi.Â PeriodÂ vii. Frequency
- Calculations on circular motion.

## Meaning of circular motion

Circular motion is the motion of a body aroundÂ a cicle. The simplest form of circular motion is theÂ 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 (Ï‰): The ratio of the angle turned through to the elapsed time.

Ï‰ = Angular velocity

Ï‰ =

The S.l unit is rad/sec

- Tangential velocity(V): This is the linear velocity in a tangential direction to the circumference.

v = =

But,Â Ï‰

ThenÂ Â Â Â Â v = rÏ‰

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 isÂ m/s^{2}

But ,Â v = rÏ‰

Then,Â a = rÏ‰^{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

orÂ Â Â F = rÏ‰^{2}= Â = 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)

orÂ Â Â F =Â – rÏ‰^{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})

## Â __Calculations on circular motion__

Question 1:Â 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.Â Centripetal acceleration

- Centripetal force
- Centrifugal force

SOLUTION

- Ï‰=

WhereÂ is the angular displacement and Ï‰ is the angular velocity

Î¸ = 360 X 2 = 720^{0}(ie two times)

Ï€ = 180^{0}

Î¸ = 4Ï€ rad

Ï‰=Â = 1.33Ï€rad/sec

- v = rÏ‰

= 3 x 1.33Ï€ = 3.99 Ï€ m/s

- m/s
^{2}

## GENERAL EVALUATION

- Explain the following terms (i)Â Angular velocityÂ (ii)Â 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