Newton’s Laws of Motion – Complete Detailed Notes with Examples & Numericals
Newton’s Laws of Motion – Complete & Detailed Notes
Newton’s Laws of Motion are the foundation of classical mechanics. These laws explain how objects move, why they move, and how forces affect motion. Almost every mechanical system we see in daily life — from walking, driving, sports, machines, and even space travel — follows these laws.
Sir Isaac Newton introduced these laws in his famous book Philosophiæ Naturalis Principia Mathematica (1687). They apply to objects moving at ordinary speeds and sizes and are extremely important for students of physics at school and undergraduate levels.
Basic Concepts Before Newton’s Laws
1. Rest and Motion
An object is said to be at rest if it does not change its position with respect to its surroundings with time. An object is said to be in motion if it changes its position with respect to its surroundings.
Rest and motion are relative terms. A person sitting in a moving bus is at rest with respect to the bus but in motion with respect to a person standing on the road.
2. Force
A force is an external agent that can change the state of rest or motion of an object, its speed, direction, or shape.
Effects of force:
- Start or stop motion
- Change speed
- Change direction
- Change shape or size
Force is a vector quantity, meaning it has both magnitude and direction.
Newton’s First Law of Motion (Law of Inertia)
Statement:
“A body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.”
This law tells us that objects do not change their motion on their own. Any change requires an external force.
Inertia
Inertia is the property of a body by virtue of which it resists any change in its state of rest or uniform motion.
Greater the mass of a body, greater is its inertia.
Types of Inertia
- Inertia of Rest: Resistance to start motion
- Inertia of Motion: Resistance to stop motion
- Inertia of Direction: Resistance to change direction
Examples of First Law
- A book remains on a table unless pushed
- Passengers fall backward when a bus starts suddenly
- Passengers fall forward when a moving bus stops
- Dust comes out when a carpet is beaten
In each case, inertia resists the change in motion.
Newton’s Second Law of Motion
Statement:
“The rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of the force.”
Momentum
Momentum is defined as the product of mass and velocity.
Momentum (p) = m × v
Momentum is a vector quantity and depends on both mass and velocity.
Mathematical Form of Second Law
Force is proportional to the rate of change of momentum:
F ∝ (Δp / Δt)
For constant mass:
F = m × a
This equation shows:
- Acceleration is directly proportional to force
- Acceleration is inversely proportional to mass
SI Unit of Force
The SI unit of force is Newton (N).
One Newton is the force that produces an acceleration of 1 m/s² in a body of mass 1 kg.
Applications of Newton’s Second Law
- Design of seat belts and airbags
- Rocket propulsion
- Sports like cricket, football, and athletics
- Braking systems of vehicles
Newton’s Third Law of Motion
Statement:
“For every action, there is an equal and opposite reaction.”
This law explains that forces always occur in pairs. When one body exerts a force on another, the second body simultaneously exerts an equal force in the opposite direction.
Key Features
- Action and reaction act on different bodies
- They are equal in magnitude
- They are opposite in direction
- They occur simultaneously
Examples of Third Law
- Walking and running
- Swimming
- Gun recoil
- Rocket motion
Common Misconceptions About Newton’s Laws
- Action and reaction cancel each other ❌ (They act on different bodies)
- Force is needed to keep motion ❌ (Force is needed to change motion)
- Heavier objects fall faster ❌ (In absence of air resistance)
Balanced and Unbalanced Forces
Balanced Forces: Net force is zero, no change in motion.
Unbalanced Forces: Net force is non-zero, causes acceleration.
Solved Numerical Examples
Example 1:
A force of 20 N acts on a mass of 4 kg. Find acceleration.
Solution:
a = F / m = 20 / 4 = 5 m/s²
Example 2:
Find momentum of a 10 kg body moving at 3 m/s.
Solution:
p = m × v = 10 × 3 = 30 kg·m/s
Practice Questions
Very Short Answer
- Define inertia.
- What is momentum?
- State Newton’s Third Law.
Short Answer
- Why do passengers fall forward when a bus stops suddenly?
- Why are action and reaction not balanced?
Numericals
- A force of 15 N acts on a mass of 3 kg. Find acceleration.
- A body of mass 2 kg moves with velocity 6 m/s. Find momentum.
Importance of Newton’s Laws
- Foundation of mechanics
- Used in engineering and technology
- Essential for understanding motion
- Basis for advanced physics
Newton’s Laws of Motion help us understand how the physical world works.
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