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Newton's Laws of Motion: First, Second & Third Law Explained

A complete Class 9 & Class 11 Physics guide to Newton's three laws of motion — inertia, F = ma, and action-reaction — with definitions of force, mass, acceleration, friction, net force, real-life examples, and solved numericals.

Physics 22 September, 2026 17 min read

Last updated: September 22, 2026

What is Motion? What is Force?

What is Motion?

Motion is the change in position of an object with respect to time and a reference point (frame of reference). An object is said to be in motion if its position changes continuously with respect to a fixed observer.

What is Force? (Force Definition)

Force is a push or pull acting on an object that can: change its state of rest or motion, change its speed, change its direction of motion, or change its shape/size. Force is a vector quantity (it has both magnitude and direction) and is measured in newtons (N) in the SI system. One newton is the force required to give a mass of 1 kg an acceleration of 1 m/s².

The study of force and laws of motion forms the foundation of classical mechanics, first formalized by Sir Isaac Newton in his 1687 work Philosophiæ Naturalis Principia Mathematica. Newton's three laws of motion explain exactly how and why objects move the way they do.

Net Force

What is Net Force?

Net force is the vector sum of all individual forces acting on an object simultaneously. Since force is a vector, forces acting in the same direction add up, while forces acting in opposite directions subtract from each other.

Net Force = Vector Sum of All Forces Block F₁ = 30 N F₂ = 10 N Net Force = 20 N (rightward)

Figure 1: Two opposing forces act on a block — a 30 N push to the right and a 10 N resistance to the left — resulting in a net force of 20 N to the right, which determines the object's acceleration.

Equilibrium: When Net Force = 0

If the net force on an object is zero, the object is said to be in equilibrium — it either remains at rest or continues moving at constant velocity. This is the direct basis of Newton's first law of motion.

Newton's First Law of Motion (Law of Inertia)

Newton's First Law — Statement

"An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force."

Newton's first law of motion, also called the Law of Inertia, was originally conceived by Galileo and later formalized by Newton. It tells us that objects do not change their state of motion on their own — a force is always required to start, stop, speed up, slow down, or change the direction of an object.

What is Inertia?

Inertia Definition

Inertia is the natural tendency of an object to resist any change in its state of rest or uniform motion. It is directly related to an object's mass — the greater the mass, the greater the inertia, and the more force is required to change its motion. This is why it's harder to push a loaded truck than an empty shopping cart.

Law of Inertia — Newton's First Law Object at Rest v = 0 Force needed Stays at rest unless pushed Object in Motion v = constant moving Force to stop Keeps moving unless stopped

Figure 2: Newton's first law in action — a resting object needs a force to start moving, and a moving object needs a force to stop, slow down, or change direction.

Everyday Examples of Newton's First Law

  • Passengers jerk forward when a bus suddenly stops (their body continues moving due to inertia).
  • A coin placed on a card over a glass falls into the glass when the card is flicked away quickly (inertia of rest).
  • Dust particles fall off a carpet when it is beaten (inertia of rest of dust vs. sudden motion of carpet fibres).
  • A ball rolling on a frictionless surface would continue forever if no force (like friction or air resistance) acted on it.

Newton's Second Law of Motion (F = ma)

Newton's Second Law — Formula

F = m × a

More generally, force equals the rate of change of momentum: F = dp/dt, where p = mv (momentum).

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is the most mathematically important of the three laws, as it allows us to calculate exactly how an object will move when forces act on it.

What is Mass?

Mass Definition

Mass is the quantity of matter contained in an object. It is a scalar quantity, measured in kilograms (kg), and remains constant regardless of location (on Earth, the Moon, or in space). Mass is also a direct measure of an object's inertia.

What is Acceleration?

Acceleration Definition

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, measured in metres per second squared (m/s²). An object accelerates when it speeds up, slows down (deceleration), or changes direction.

a = (v − u) / t

Newton's Second Law: F = ma m = 2 kg F = 10 N a = 5 m/s² (light mass → more acceleration) m = 20 kg F = 10 N a = 0.5 m/s² (heavy mass → less acceleration)

Figure 3: The same 10 N force produces very different accelerations depending on mass — a 2 kg object accelerates at 5 m/s², while a 20 kg object accelerates at only 0.5 m/s², illustrating a = F/m.

Everyday Examples of Newton's Second Law

  • It's easier to push an empty shopping cart than a fully loaded one (same force, different mass, different acceleration).
  • A cricket ball accelerates more than a bowling ball when hit with the same force.
  • Cars with more powerful engines (greater force) accelerate faster for the same vehicle mass.

Newton's Third Law of Motion (Action-Reaction)

Newton's Third Law — Statement

"For every action, there is an equal and opposite reaction."

Newton's third law of motion states that whenever one object exerts a force (the "action") on a second object, the second object simultaneously exerts a force of equal magnitude but opposite direction (the "reaction") back on the first object.

Important: Action and Reaction Act on Different Objects

A common misconception is that action-reaction pairs cancel out. They do not, because they act on two different objects, not the same object. This is why a rocket can still accelerate forward even though the exhaust gases push backward with equal force.

Newton's Third Law: Action & Reaction Object A Object B Action: A pushes B Reaction: B pushes A back Equal magnitude, opposite direction — acting on two different objects

Figure 4: Action-reaction pairs always act on two different objects with equal magnitude and opposite direction, such as a swimmer pushing water backward (action) while the water pushes the swimmer forward (reaction).

Everyday Examples of Newton's Third Law

  • A swimmer pushes water backward to move forward.
  • A rocket expels gas downward/backward and is propelled upward/forward.
  • When you jump off a small boat, the boat moves backward as you move forward.
  • Walking: your foot pushes the ground backward, and the ground pushes your foot forward.
  • A gun recoils backward when a bullet is fired forward.

The Three Laws of Motion — Summary Table

LawStatement (Short)Key FormulaKey Idea
First Law (Law of Inertia)Objects resist changes in motionFnet = 0 ⇒ constant velocityInertia
Second LawForce causes acceleration, proportional to massF = maCause of acceleration
Third LawEvery action has an equal, opposite reactionFAB = −FBAAction-reaction pairs

Friction

What is Friction?

Friction is the force that opposes the relative motion (or tendency of motion) between two surfaces in contact. It acts parallel to the surfaces and in a direction opposite to the motion or applied force. Friction is a direct, everyday application of Newton's laws — it is one of the real external forces that must be accounted for in the net force when applying F = ma.

Types of Friction

  • Static friction — opposes the start of motion between two surfaces at rest relative to each other.
  • Kinetic (sliding) friction — opposes motion between two surfaces already sliding against each other.
  • Rolling friction — opposes motion when one surface rolls over another (generally much smaller than sliding friction).

Why Friction Matters for Newton's Laws

Without friction, Newton's first law would be easy to observe directly (objects would slide forever once set in motion). In real life, friction is usually the hidden force that eventually brings moving objects to rest, and it must be included when calculating the net force in Newton's second law problems.

Mass vs Weight & Connection to Gravity

A common confusion in the study of Newton's laws is the difference between mass and weight:

PropertyMassWeight
DefinitionAmount of matter in an objectGravitational force acting on that mass
Formula—W = mg
SI UnitKilogram (kg)Newton (N)
Quantity TypeScalarVector
Varies with location?No (constant everywhere)Yes (depends on local gravity g)

Weight is simply a special case of Newton's second law, where the force is due to gravity: F = mg, where g ≈ 9.8 m/s² on Earth's surface. This is why an astronaut's mass stays the same on the Moon, but their weight is about one-sixth of their Earth weight, since the Moon's gravitational acceleration is much smaller.

Real-Life Examples of Newton's Laws

SituationLaw Illustrated
Wearing a seatbelt in a car during sudden brakingFirst Law (Inertia)
A heavier vehicle needs more force to reach the same accelerationSecond Law (F = ma)
A rocket launching into spaceThird Law (Action-Reaction)
Kicking a football harder makes it accelerate fasterSecond Law (F = ma)
Walking on the groundThird Law (Action-Reaction)
A book resting on a table stays at restFirst Law (Net Force = 0)

Who Was Isaac Newton?

Sir Isaac Newton (1643–1727) was an English mathematician, physicist, and astronomer widely regarded as one of the most influential scientists of all time. In 1687, he published Philosophiæ Naturalis Principia Mathematica (commonly known as the Principia), in which he formulated his three laws of motion and the law of universal gravitation. His laws of motion remain the foundation of classical mechanics and are still taught in physics classrooms worldwide today, over three centuries later.

Class 9 vs Class 11: How the Syllabus Differs

Newton's laws of motion are taught at two levels in the Indian NCERT curriculum, with increasing depth:

AspectClass 9 (Force and Laws of Motion)Class 11 (Laws of Motion)
FocusConceptual introduction, qualitative understandingRigorous, mathematical treatment with vectors
MomentumBasic definition (p = mv)Conservation of momentum, impulse, derivations
FrictionQualitative discussionCoefficient of friction, angle of friction, banking of roads
ApplicationsEveryday examplesCircular motion, pseudo forces, equilibrium of concurrent forces

This article covers the core concepts common to both levels, forming a strong foundation whether you're encountering Newton's laws for the first time in Class 9 or studying them in greater mathematical depth in Class 11.

Solved Numerical Problems

Problem 1: Finding Force Using F = ma

Question: A car of mass 1000 kg accelerates from rest to 20 m/s in 10 seconds. Find the net force acting on the car.

Solution:

Given: m = 1000 kg, u = 0, v = 20 m/s, t = 10 s

Acceleration: a = (v − u)/t = (20 − 0)/10 = 2 m/s²

Using Newton's second law: F = ma = 1000 × 2 = 2000 N

Problem 2: Finding Acceleration Given Mass and Force

Question: A net force of 50 N acts on an object of mass 5 kg. Find its acceleration.

Solution:

Given: F = 50 N, m = 5 kg

Using F = ma: a = F/m = 50/5 = 10 m/s²

Problem 3: Net Force with Friction Opposing Motion

Question: A box of mass 10 kg is pushed with a force of 40 N. If a frictional force of 15 N opposes the motion, find the resulting acceleration of the box.

Solution:

Net force: Fnet = Applied force − Friction = 40 − 15 = 25 N

Using Fnet = ma: a = Fnet/m = 25/10 = 2.5 m/s²

Problem 4: Newton's Third Law — Recoil

Question: A bullet of mass 0.05 kg is fired from a gun of mass 5 kg with a velocity of 200 m/s. Find the recoil velocity of the gun.

Solution:

By conservation of momentum (a consequence of Newton's third law), initial momentum = 0, so momentum of bullet = −momentum of gun.

mbullet × vbullet = −mgun × vgun

0.05 × 200 = −5 × vgun

vgun = −10/5 = −2 m/s

Result: The gun recoils backward with a velocity of 2 m/s, in the direction opposite to the bullet.

Quick Revision Summary

First LawObjects resist change in motion (inertia); Fnet = 0 ⇒ no acceleration
Second LawF = ma — force determines acceleration
Third LawEvery action has an equal and opposite reaction, on two different bodies
Weight vs MassW = mg — weight depends on gravity, mass does not

Frequently Asked Questions (FAQ)

Newton's three laws of motion are: First Law (Law of Inertia) — objects resist changes to their state of motion unless acted on by a net force. Second Law — F = ma, force equals mass times acceleration. Third Law — for every action, there is an equal and opposite reaction.

Newton's first law states that an object at rest stays at rest, and an object in motion continues at constant velocity, unless acted upon by a net external force. It defines inertia as an object's resistance to changes in its state of motion.

Newton's second law states that acceleration is directly proportional to net force and inversely proportional to mass, expressed as F = ma. More generally, force equals the rate of change of momentum, F = dp/dt.

Newton's third law states that for every action, there is an equal and opposite reaction. When one object exerts a force on another, the second object exerts an equal and opposite force back on the first — and these forces act on two different objects.

Inertia is the natural tendency of an object to resist changes in its state of rest or motion. It is directly related to mass — heavier objects have more inertia and require more force to change their motion.

Force is a push or pull that can change an object's state of rest or motion, its speed, its direction, or its shape. It is a vector quantity measured in newtons, defined by F = ma.

Net force is the vector sum of all forces acting on an object. It determines the object's resulting acceleration via Newton's second law; if net force is zero, the object is in equilibrium.

Mass is the amount of matter in an object (constant everywhere, measured in kg). Weight is the gravitational force on that mass (W = mg, measured in newtons), and varies with location due to differences in gravitational acceleration.

Friction is the force that opposes relative motion between two surfaces in contact. It acts opposite to the direction of motion or applied force, and must be included as part of the net force when applying Newton's second law.

Related Topics in Physics

Wheatstone Bridge Convex & Concave Lens Momentum & Impulse Friction Circular Motion Gravitation Work, Energy & Power Class 9 Physics Class 11 Physics