MOTION ( CLASS 9TH PHYSICS CBSE NCERT)

MOTION ( CLASS 9TH PHYSICS CBSE NCERT)

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 Core Idea

• Motion is defined as change in position of an object with time.
• To describe motion, we must compare the position of an object with respect to a reference point.
• Without a reference point, we cannot decide whether an object is at rest or in motion.
• Motion is relative, meaning it depends on the observer.

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 Spotlight

 Reference Point (Origin)

• A fixed point used to describe position of an object.
• Also called origin.

 Example:

• A school is 2 km north of a railway station
  → Railway station = reference point

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 Motion is Relative

 Example:

• Passenger inside a moving bus:
• Relative to bus → at rest
• Relative to road → in motion

 Same object → different observations

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 Motion Along Straight Line

• Simplest type of motion where an object moves along a straight path

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 Distance vs Displacement

• Distance → total path covered by the object (scalar quantity)
• Displacement → shortest distance between initial and final position (vector quantity)

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 Brain Booster

• Distance is always positive, but displacement can be zero
• If an object returns to its starting point:
• Distance ≠ 0
• Displacement = 0
• Motion depends on observer’s frame of reference
• Same object can be at rest and in motion simultaneously

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 Let’s Check Your Thinking

1. Why can’t we define motion without a reference point?
2. A person sitting in a moving bus — is he at rest or in motion? Explain.
3. Can an object be at rest and in motion at the same time? How?
4. Give one real-life example showing motion is relative.
5. If an object comes back to its starting point, what will be its displacement?

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Motion cannot be defined without a reference point because motion is the change in position relative to something, so without comparison it has no meaning. A person sitting in a moving bus is at rest relative to the bus but in motion relative to the ground, which shows that motion depends on the observer. Yes, an object can be at rest and in motion at the same time depending on the reference frame, for example, a passenger in a train. A real-life example of relative motion is trees appearing to move backward when we sit inside a moving vehicle. If an object comes back to its starting point, its displacement becomes zero because initial and final positions are the same, even though distance travelled is not zero.

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 MOTION ALONG A STRAIGHT LINE

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 Core Idea

• The simplest type of motion is motion along a straight line, also called linear motion.
• In this motion, an object moves along a single straight path.
• To describe this motion, we use two important quantities: distance and displacement.

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 Spotlight

 Straight Line Motion

• Motion in which an object moves along a straight path.
   Example: A car moving on a straight road.

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 Distance

• The total length of the path travelled by an object.
• It is a scalar quantity (only magnitude, no direction).
• Always positive.

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 Displacement

• The shortest distance between initial and final position.
• It has direction, so it is a vector quantity.
• Can be positive, negative, or zero.

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 Understanding Distance vs Displacement

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 Important Concept (NCERT Type Example)

• Object moves:
• O → A = 60 km
• A → B = 25 km (backward)

 Distance = 60 + 25 = 85 km
 Displacement = 35 km

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 Special Case

• If an object returns to its starting point:

 Distance = total path travelled
 Displacement = 0

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 Distance vs Displacement

Distance	Displacement
Total path covered	Shortest path
Scalar quantity	Vector quantity
Always positive	Can be zero
Depends on path	Depends only on initial & final position

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 Brain Booster

• Distance is always greater than or equal to displacement
• Displacement can never be greater than distance
• If motion is in a straight line in one direction:
• Distance = Displacement
• If direction changes:
• Distance > Displacement

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 Let’s Check Your Thinking

1. Can distance and displacement be equal? When?
2. Can displacement be greater than distance?
3. A person walks 10 m east and then 10 m west. Find distance and displacement.
4. Why is displacement a vector quantity?
5. If an object moves in a straight line without changing direction, what is the relation between distance and displacement?

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Distance and displacement are equal when an object moves in a straight line in one direction without changing direction. Displacement can never be greater than distance because it represents the shortest path between two points. If a person walks 10 m east and then 10 m west, the total distance is 20 m but displacement is zero because the initial and final positions are the same. Displacement is a vector quantity because it includes both magnitude and direction. When an object moves in a straight line without changing direction, distance is equal to displacement.

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UNIFORM AND NON-UNIFORM MOTION

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 Core Idea

• Objects do not always move in the same way.
• Sometimes motion is regular (uniform) and sometimes irregular (non-uniform).
• This classification is based on how distance changes with time.

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 Spotlight

 Uniform Motion

• An object is said to be in uniform motion if it covers equal distances in equal intervals of time.

 Example:

• A car moving at constant speed on a straight road

 Key Point:

• Speed remains constant
• Motion is regular

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 Non-uniform Motion

• An object is said to be in non-uniform motion if it covers unequal distances in equal intervals of time.

 Example:

• A car moving in traffic (speed keeps changing)

 Key Point:

• Speed is not constant
• Motion is irregular

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 Understanding Uniform vs Non-uniform Motion

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 Important Comparison

Uniform Motion	Non-uniform Motion
Equal distance in equal time	Unequal distance in equal time
Speed is constant	Speed changes
Straight-line motion (generally)	May change direction or speed

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 Brain Booster

• Uniform motion is ideal, rarely seen perfectly in real life
• Most motions around us are non-uniform
• Even if direction changes at constant speed → motion becomes non-uniform
• Uniform motion means no change in speed, not necessarily no change in direction

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 Let’s Check Your Thinking

1. What is uniform motion? Give one example.
2. What is non-uniform motion? Give one example.
3. Can a body have uniform motion in real life? Explain.
4. If an object covers equal distances in unequal time intervals, what type of motion is it?
5. A car moves faster and slower at different times. What type of motion is this?

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Uniform motion is when an object covers equal distances in equal intervals of time, such as a car moving with constant speed on a straight road. Non-uniform motion occurs when an object covers unequal distances in equal intervals of time, such as a car moving in traffic. In real life, perfectly uniform motion is rare because speed usually changes due to various factors. If an object covers equal distances in unequal time intervals, it is also considered non-uniform motion because speed is not constant. When a car moves faster and slower at different times, it shows non-uniform motion.

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SPEED AND VELOCITY

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 Core Idea

• To describe motion more precisely, we need to know how fast an object is moving.
• This is given by speed and velocity.
• Both relate distance/displacement with time, but they are not the same.

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 Spotlight

 Speed

• Speed is defined as the distance travelled per unit time.

 Formula:

 

 

• It is a scalar quantity (no direction)
• Always positive

 Example:

• A car covers 100 km in 2 hours → speed = 50 km/h

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 Velocity

• Velocity is defined as the displacement per unit time.

 Formula:

 

 

 

• It is a vector quantity (has direction)
• Can be positive, negative, or zero

 Example:

• 50 km/h towards north → velocity

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 Understanding Speed vs Velocity

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 Important Case

• If an object returns to starting point:

 Distance ≠ 0 → Speed exists
 Displacement = 0 → Velocity = 0

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 Average Speed

 

 

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 Average Velocity

 

 

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 Uniform Velocity

• When an object moves with:
• constant speed
• in a fixed direction

 Then velocity is uniform

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 Brain Booster

• Speed tells how fast, velocity tells how fast + in which direction
• Speed can never be negative, but velocity can
• If direction changes → velocity changes (even if speed same)
• Circular motion has constant speed but changing velocity

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Let’s Check Your Thinking

1. What is the difference between speed and velocity?
2. Can velocity be zero while speed is not? Explain.
3. A person walks 10 m east and then 10 m west in 5 seconds. Find average speed and velocity.
4. What is uniform velocity?
5. Why is velocity a vector quantity?

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Speed is the distance travelled per unit time and has no direction, while velocity is displacement per unit time and includes direction. Velocity can be zero while speed is not, for example when an object returns to its starting point, displacement becomes zero but distance is not zero. If a person walks 10 m east and then 10 m west in 5 seconds, total distance is 20 m so average speed is 4 m/s, but displacement is zero so average velocity is zero. Uniform velocity means constant speed in a fixed direction. Velocity is a vector quantity because it has both magnitude and direction.

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 SPEED WITH DIRECTION (VELOCITY)

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🔵 Core Idea

• When speed is specified along with direction, it is called velocity.
• Velocity tells not only how fast an object is moving, but also in which direction it is moving.
• Therefore, velocity is a vector quantity.

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 Spotlight

 Definition of Velocity

• Velocity is the speed of an object in a given direction.

 Or mathematically:

 

 

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 Difference from Speed

• Speed → only magnitude (how fast)
• Velocity → magnitude + direction

 Example:

• 60 km/h → speed
• 60 km/h towards north → velocity

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 Direction Matters

• Even if speed is constant, velocity can change if direction changes

 Example:

• A car moving in a circular path:
• Speed = constant
• Velocity = changing (because direction changes)

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 Understanding Velocity (Direction Concept)

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 Types of Velocity

1. Uniform Velocity

• When both speed and direction remain constant

2. Non-uniform Velocity

• When either speed or direction (or both) change

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 Brain Booster

• Velocity changes if:
• Speed changes
• Direction changes
• Circular motion = constant speed but changing velocity
• Velocity can be:
• Positive
• Negative
• Zero

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 Let’s Check Your Thinking

1. What is meant by speed with direction?
2. Why is velocity called a vector quantity?
3. Can velocity change even if speed is constant? Explain.
4. Give one example where speed is constant but velocity changes.
5. What is uniform velocity?

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Speed with direction is called velocity, which describes both how fast an object is moving and in which direction. Velocity is a vector quantity because it has both magnitude and direction. Velocity can change even if speed remains constant, because a change in direction also changes velocity. A common example is circular motion, where speed remains constant but direction keeps changing. Uniform velocity occurs when both speed and direction remain constant throughout the motion.

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RATE OF CHANGE OF VELOCITY (ACCELERATION)

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 Core Idea

• When the velocity of an object changes, we say the object is accelerating.
• Acceleration is defined as the rate of change of velocity with time.
• A change in velocity can occur due to:
• Change in speed
• Change in direction
• Change in both

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 Spotlight

 Definition of Acceleration

• Acceleration is the change in velocity per unit time.

 Formula:

 

 

Where:

• ( u ) = initial velocity
• ( v ) = final velocity
• ( t ) = time
• ( a ) = acceleration

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 Types of Acceleration

1. Uniform Acceleration

• When velocity changes by equal amounts in equal intervals of time

 Example:

• A freely falling object

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2. Non-uniform Acceleration

• When velocity changes by unequal amounts in equal intervals of time

 Example:

• A car moving in traffic

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 Deceleration (Retardation)

• When velocity decreases with time, acceleration is negative
• This is called deceleration or retardation

 Example:

• A car slowing down

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🖼️ Understanding Acceleration

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 Important Observations

• If velocity is constant → acceleration = 0
• If speed changes → acceleration exists
• If direction changes → acceleration exists (even if speed same)

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 Brain Booster

• Acceleration depends on velocity, not just speed
• Circular motion has constant speed but still acceleration
• Negative acceleration = slowing down
• Unit of acceleration = m/s²

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 Let’s Check Your Thinking

1. What is acceleration?
2. Can an object have acceleration without change in speed? Explain.
3. What is uniform acceleration?
4. What is retardation?
5. A car slows down with time. What type of acceleration is this?

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Acceleration is the rate of change of velocity with time. An object can have acceleration even without change in speed if its direction changes, such as in circular motion. Uniform acceleration occurs when velocity changes by equal amounts in equal intervals of time. Retardation is negative acceleration in which velocity decreases with time. When a car slows down, it experiences retardation or negative acceleration.

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GRAPHICAL REPRESENTATION OF MOTION

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Core Idea

• Motion can be understood more clearly using graphs.
• Graphs show how one physical quantity changes with respect to another.
• In this chapter, we mainly study:
• Distance–Time Graph
• Velocity–Time Graph

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 Spotlight

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 Distance–Time Graph

• It shows how distance changes with time

 Case 1: Uniform Motion

• Distance increases uniformly with time
• Graph is a straight line

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 Distance–Time Graph (Uniform Motion)

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 Case 2: Non-uniform Motion

• Distance does not increase uniformly
• Graph is a curve

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Distance–Time Graph (Non-uniform Motion)

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 Velocity–Time Graph

• It shows how velocity changes with time

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 Case 1: Uniform Velocity

• Velocity remains constant
• Graph is a straight horizontal line

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 Velocity–Time Graph (Uniform Velocity)

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 Case 2: Uniform Acceleration

• Velocity increases uniformly
• Graph is a straight sloping line

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 Velocity–Time Graph (Uniform Acceleration)

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 Case 3: Non-uniform Acceleration

• Velocity changes irregularly
• Graph is a curve

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Velocity–Time Graph (Non-uniform Acceleration)

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 Important Results from Graphs

• Slope of distance–time graph → speed
• Slope of velocity–time graph → acceleration
• Area under velocity–time graph → distance travelled

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 Brain Booster

• Steeper line → greater speed
• Horizontal line (distance-time) → object at rest
• Horizontal line (velocity-time) → constant velocity
• Area under graph gives physical meaning (distance)
• Graphs help in solving numerical problems easily

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Let’s Check Your Thinking

1. What does the slope of a distance–time graph represent?
2. What does the slope of a velocity–time graph represent?
3. What does the area under a velocity–time graph represent?
4. How can you identify uniform motion from a graph?
5. What type of graph represents non-uniform motion?

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The slope of a distance–time graph represents speed, while the slope of a velocity–time graph represents acceleration. The area under a velocity–time graph represents the distance travelled by the object. Uniform motion is represented by a straight line in a distance–time graph and a horizontal line in a velocity–time graph. Non-uniform motion is represented by a curved line in both graphs, indicating changing speed or acceleration.

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EQUATIONS OF MOTION

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 Core Idea

• For an object moving with uniform acceleration, we can describe its motion using mathematical equations called equations of motion.
• These equations relate:
• Initial velocity (u)
• Final velocity (v)
• Acceleration (a)
• Time (t)
• Displacement (s)

 These equations are valid only for uniform acceleration.

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 Spotlight

 First Equation of Motion

v = u + at

 It shows how velocity changes with time

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 Second Equation of Motion

 

 It gives displacement in given time

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 Third Equation of Motion

 

 It relates velocity and displacement (without time)

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 Graphical Interpretation

 From velocity–time graph:

• Slope → acceleration
• Area → displacement

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 Important Observations

• If a = 0 → motion is uniform → v = u
• If u = 0 → object starts from rest
• Equations are used to solve numerical problems

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 Brain Booster

• These equations are valid only when:
• Acceleration is constant
• If motion is not uniform → equations cannot be used directly
• Most exam numericals are based on:
• Substituting values correctly
• Always follow sign convention

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 Let’s Check Your Thinking

1. Write the three equations of motion.
2. When are these equations valid?
3. What happens if acceleration is zero?
4. Which equation is used when time is not given?
5. An object starts from rest and accelerates uniformly. Which equation will you use to find displacement?

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The three equations of motion are v = u + at, s = ut + ½at², and v² = u² + 2as. These equations are valid only when acceleration is uniform or constant. If acceleration is zero, the object moves with constant velocity and v = u. When time is not given, the third equation v² = u² + 2as is used. If an object starts from rest and we need to find displacement, the second equation s = ut + ½at² is used, where u = 0.

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UNIFORM CIRCULAR MOTION

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 Core Idea

• When an object moves along a circular path with constant speed, the motion is called uniform circular motion.
• Even though the speed is constant, the object is said to be accelerating because its direction keeps changing.

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 Spotlight

 Definition

• Uniform circular motion is the motion of an object in a circular path at constant speed.

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 Why is it Accelerated Motion?

• Velocity depends on speed + direction
• In circular motion:
• Speed → constant
• Direction → continuously changing

 Therefore, velocity changes → acceleration exists

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Understanding Uniform Circular Motion

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 Direction of Velocity

• At any point on the circle, velocity acts along the tangent to the path

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 Direction of Acceleration

• Acceleration always acts towards the centre of the circle
• This is called centripetal acceleration

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 Examples

• Motion of a satellite around Earth
• A stone tied to a string and rotated
• Car moving on a circular track
• Fan blades rotating

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 Brain Booster

• Constant speed ≠ constant velocity
• Circular motion always has acceleration
• If the string breaks → object moves in straight line (tangent)
• Acceleration in circular motion is always towards centre

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 Let’s Check Your Thinking

1. What is uniform circular motion?
2. Why is circular motion called accelerated motion even at constant speed?
3. In which direction does velocity act in circular motion?
4. What happens if the string breaks while rotating a stone?
5. Give two real-life examples of circular motion.

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Uniform circular motion is the motion of an object along a circular path with constant speed. It is called accelerated motion because even though the speed remains constant, the direction of velocity keeps changing, which means velocity is changing. In circular motion, velocity always acts along the tangent to the path, while acceleration acts towards the centre of the circle. If the string breaks while rotating a stone, the object moves in a straight line along the tangent. Examples include a satellite revolving around the Earth and a stone tied to a string and rotated.