## What is Circular Motion

When an object moves in a circle, it is called Circular Motion

Example

An athlete taking a round of a circular park

## What is Uniform Circular Motion

If an object moves in a circular path with uniform speed, it is called Uniform Circular Motion

Examples

Motion of Moon(Moon Moving around the earth)

Motion of Earth(Earth Moving around the sun)

A cyclist on circular track

## What is Constant in Uniform Circular Motion - Speed or Velocity?

In Uniform Circular Motion, speed is constant

As our object keeps on changing direction, velocity keeps on changing.

So,velocity cannot be constant.

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Explanation
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Let's take different tracks

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Rectangular Track
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If an athlete travels rectangular track ABCD, he has to change direction 4 times

AB, BC, CD, DA

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Hexagonal Track
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Similarly in Hexagonal track ABCDEF,

athlete has to change direction 6 times

AB, BC, CD, DE, EF, FA

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Octagonal Track
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Similarly in Octagon ABCDEFGH

Athlete has to change direction 8 Times

AB, BC, CD, DE, EF, FG, GH, HA

Hence, as number of sides increase

, athlete has to change direction more number of times

Similarly if we keep on increasing sides, it becomes shape of a circle

It can be said that circle contains infinite number of sides

An athlete moving in a circular changes direction infinite number of times

## Why is Uniform Circular Motion always called accelerated motion

If a person travels in uniform circular motion, its magnitude of velocity(speed) remains constant

However, direction of motion keeps on changing indefinitely

Hence Uniform Motion is called Accelerated Motion

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Example 1
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An athlete running in a circular track with uniform speed keeps on changing direction infinite number of times

Since direction keeps on changing,it is accelerated motion

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Example 2
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A toy train moves in a circular path at constant speed but direction of toy train keeps on changing indefinite number of times

Since direction keeps on changing,it is accelerated motion

How to Calculate Distance and speed in case of Circular Motion

We know that

Circumference of Circle = 2πr

where r is radius of Circle

So Distance travelled by a body moving in a Circular Path

= Circumference of Circle

= 2πr

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Example 1
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Suppose a person takes a round of circular park whose Diameter is 140 Meters

What is Distance covered by Person

Diameter = 140 meters

Radius = Diameter/2 = 140/2 = 70 meters

Distance travelled by a person =

= 2πr

= 2 × 22/7 × 70

= 440 meters

## How to Calculate Speed/Velocity in case of Circular Motion

We know that

Speed = Distance/Time

in Circular Motion,Distance = 2πr ,So

Speed = 2πr / Time

Formula of Velocity is also same

Velocity = 2πr/Time

v = 2πr/t

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Example 2
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Suppose a person takes a round of circular park whose Diameter is 140 Meters in 2 minutes

What is Distance covered by Person

What is speed of Person

Distance travelled by a person=

= 2πr

= 2 × 22/7 × 70

= 440 meters

Time Taken = 2 minutes = 120 seconds

Formula of Velocity is also same

Velocity = 2πr/Time

v = 2 π r/t

v = 440/120

v = 3.67 meters/second

## Direction of Acceleration and Velocity in Circular Motion

In Circular Motion,

- Acceleration is always towards the center
- Velocity is always along tangent

In the figure, we can see the direction of velocity and acceleration at different points in circular motion

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