Newton’s First Law of Motion (Law of Inertia): Definition, Examples & Applications

Why do things keep moving until something stops them or why do things continue to be in rest until it is disturbed? From a sliding coffee cup in the morning to a drifting satellite around the globe which helps us in many ways, the answer is the same: inertia. Newton’s First Law of Motion—the law of inertia—says objects stay at rest or move uniformly unless a net external force acts. Below, we’ll unpack this with plain language, simple math, and everyday examples.

Introduction to Newton’s First Law of Motion

Ever slammed the brakes or felt falling towards forward when the driver hits the brake in a running vehicle? Or ever tried shaking clothes to let the dust particles on it go away. You are right, that all is happening due to Newton’s First Law of Motion which explains these processes by the term, inertia. That “keep doing what you were doing” feeling is inertia. Newton’s First Law of Motion—often called the Law of Inertia—captures this everyday truth in precise language: if the net external force on an object is zero, its velocity stays constant (it remains at rest or moves in a straight line at steady speed). In symbols: \(\sum F = 0\) which implies, \(v = constant\) . In this article, we’ll build intuition first, then connect it to the simple math behind the idea.

Newton organized the rules of motion into three elegant laws:

• First Law (Inertia): The object will continue to be at rest or motion unless an external force or any entity has not disturbed it.
• Second Law (Dynamics): Force acting on any object can be expresses as the producto of mass of that body and acceleration experienced by that body itself. \(F=ma\).
• Third Law (Action–Reaction): To each and every action there is equal and opposite reaction, which clarifies that the forces come in equal and opposite pairs.

Together, these laws explain how and why objects start, stop, and change direction—from a rolling football to orbiting satellites.

Historical Background

Centuries before Newton, according to Aristotle (384-322 BCE) a continuous force was necessary to keep an object in motion. As per his explanations, every moving body required a ‘mover’ to sustain its motion, and once the force was removed, the body would naturally come to rest. There were several examples he had noticed to support his this claims like, carts stop when you stop pushing, arrows fall when the bow’s force is spent. He had separated two types of motions, a natural motion (a stone falling toward its natural place) and a violent motion which includes pushing, pulling, throwing. Generally termed as violent theory dominated physics for nearly 2000 years. — because friction and air resistance quietly made it seem true.

This explanation of Aristotle was challenged by Galileo Galilei (1564-1642) with the help of several experiments, especially with inclined planes, because free fall is too fast to be timed by the human eye. He observed that if the objects are set on a smooth surface, once set in motion, they will continue to move further with less force. Now, push this thought to the ideal limit — no friction, no air drag — and the ball would never stop or change direction on its own. Galileo extracted the law of uniformly accelerated motion: s ∝ t², v ∝ t. That stubborn persistence is inertia: a body keeps its state of rest or uniform straight-line motion unless an external force interferes. Galileo’s insight replaced guesswork with experiment and cleared the runway for Newton’s First Law.

Sir Issac Newton (1642 – 1727) used Galileo Galilei’s theory as a reference to develop his universal statement: an object remains at rest or in uniform straight-line motion unless acted upon by a net external force. He also framed this within a mathematical system that connects forces to acceleration (Second Law) and explains interactions (Third Law), giving us a compact criterion \(\sum F = 0\) which implies \(v = constant\)  which anchors all of classical mechanics.

Statement of Newton’s First Law

Importance

• It shows an equivalence between ‘state of rest’ and ‘state of uniform motion along a straight line’ as both need a net unbalanced force to change the state. Both these are referred to as ‘state of motion’. The distinction between state of rest and uniform motion lies in the choice of the ‘frame of reference’.
• It defines force as an entity (or a physical quantity) that brings about a change in the ‘state of motion’ of a body, i.e., force is something that initiates a motion or controls a motion. Second law gives its quantitative understanding or its mathematical expression.
• It defines inertia as a fundamental property of every physical object by which the object resists any change in its state of motion. Inertia is measured as the mass of the object. More specifically it is called inertial mass, which is the ratio of net force to the corresponding acceleration.

Mathematical Representation of First Law

As the core idea for Newton’s First Law of motion, if the net external force is zero, motion doesn’t change. 

\(\sum F = 0\) → \(a_0\) → \(v = constant\)

Equation for rest: If an object is at rest and \(\sum F=0\), then \(a=0\) and it stays at rest \((v=0)\).

Equation for uniform motion: If an object is in motion and \(\sum F=0\), then \(a=0\)  and velocity stays the same. (same speed and straight-line direction) 

• As the net force is 0, and from the Newton’s second law \(F=ma\), the first law can be considered as a zero-acceleration case, expressing inertia: no net force → no change in motion.

Inertia and its types

The tendency of an object to stay in its respective state is generally termed as inertia. Generally, it resists any change in the state. Inertia and force are opposite entities. It is not a force, it’s a property of matter. The heavier the objects, the harder it is to start/stop or turn. For spinning objects, the resistance is set by the moment of inertia.

Inertia of Rest: The tendency of any object to remain at rest unless any external force acts on it is called the inertia of rest.

• A coin kept on a card drops in a glass of water if the card is removed at speed.
• Dust stays put when a rug is yanked, so it seems to “fly off”.

Inertia of motion:  The tendency of an object to keep moving with the same speed in a straight line unless a net force acts is the inertia of motion.

• A hockey puck glides far on smooth ice.
• Luggage on a car roof wants to continue forward if the car brakes hard –seatbelts/straps counter this.

Inertia of Direction: The tendency of an object to keep the same direction of motion unless an external force turns it.

• In a sharp turn, passengers feel thrown outward; their bodies want to keep going straight.
• A stone released from a whirling string flies tangentially.

Effect of Force and Equilibrium

The core idea of Newton’s first law is that the motion of an object can only change when the net external force is non-zero. In real life, many forces are acting all at once on any object (weight, normal, friction, tension). What really matters is the vector sum  – not any single force in isolation.

External Vs Internal Forces

Forces that are exerted on the system by things outside the system are external; forces between parts inside the system are internal forces.

Real-life examples of Newton’s First Law

1. Book on a Table:

• A book stays where it is until someone applies force to move it. The scenario of the book on the table illustrates both parts of Newton’s First Law: 
• An object at rest stays at rest: The book remains motionless until you, or some other external force, acts upon it.
• An object in motion stays in motion: If the book were sliding across a frictionless table, it would continue to move in a straight line at a constant speed forever. The reason a book does eventually stop on a regular table is that another force, friction, brings it to a halt.

2. Passenger in a Bus:

• When a moving bus suddenly stops, passengers tend to fall forward because their bodies try to keep moving. This observation is a perfect illustration of Newton’s First Law of Motion, also known as the law of inertia.
• How inertia explains the passenger’s motion?

• Before the brakes are applied: The bus and the passengers are all in a state of uniform motion, traveling at the same constant velocity.
• When the bus stops: The bus’s brakes apply a large, sudden force that rapidly brings the bus to a stop. This force acts on the bus and, through friction, on the passengers’  feet and the part of their body touching the seat.
• The effect of inertia: The passengers’ upper bodies, however, are not directly connected to the bus’s braking system. According to the law of inertia, they tend to continue moving forward at the bus’s original speed because no force has acted on them yet to change their state of motion.

3. Ball Rolling on Ground:
   A rolling ball gradually stops due to friction, which is the external force.

• The Initial Push: When you first push or roll the ball, you apply an initial force that sets it in motion.
• The Law of Inertia (Ideal Scenario): If there were no external forces—meaning a perfectly smooth, frictionless surface with no air resistance—the ball would continue to roll forever at a constant velocity.
• Friction and Air Resistance (Real-World Scenario): In reality, two main external forces act on the ball to slow it down and stop it:
• Friction:
• The contact force between the ball and the ground opposes the ball’s motion. This resistance, known as rolling friction, arises from minor deformations in the surfaces of both the ball and the ground.
• Air Resistance (Drag): 
• The air surrounding the ball pushes against it, also opposing its motion. This effect is more significant for faster-moving objects.

4. Hanging Clothes:
   When we shake a cloth, dust particles fall off because they tend to remain in their state of rest while the cloth moves.

• Initial State: Before you shake the cloth, both the cloth and the dust particles resting on its surface are in a state of rest.
• The Shake: When you shake the cloth, you apply a sudden, external force to the cloth, causing it to move rapidly.
• Inertia in Action: The dust particles, due to their inertia of rest, tend to stay in their initial state of rest. They resist the sudden movement of the cloth.
• Separation: Since the dust particles are not securely bound to the fabric, the fast-moving cloth moves out from under them. Because they remain in place due to their inertia, the dust particles become separated from the cloth.
• Falling: Once separated from the cloth, the force of gravity pulls the dust particles downward, causing them to fall to the ground.

5. Car Seatbelt:
   Seatbelts protect passengers from moving forward suddenly during a crash by applying an opposing force.

• Initial motion: When a car is moving, both the vehicle and its passengers are in motion at the same velocity.
• The crash: In a collision, the car is forced to stop almost instantly, but because of inertia, the passengers’ bodies continue to move forward at the car’s original speed.
• The threat: Without a seatbelt, the unrestrained passengers would collide with the steering wheel, dashboard, or windshield. Being ejected from the vehicle is also a major risk and is almost always deadly. 

Applications and Significance

In this evolving world of technology, Newton’s First Law tells us when motion will change and when it won’t. Engineers use it to design things that move smoothly – from robot arms and conveyor belts to trains and drones. By reducing the unwanted pushes and pulls (friction, drag), machines work more efficiently, last longer, and use less energy.

Importance in Physics and Engineering

• Robots and Drones move smoothly by keeping the net force near zero and only pushing when a change is needed.
• 3D printers/CNC machines reduce friction so parts glide and stop exactly where told.
• Phones and watches use tiny sensors (accelerometers/gyroscopes) to spot any sudden change from steady motion.

Safety mechanisms and technology

• Car use seatbelts, airbags, headrests, and crumple zones to manage your body’s inertia in a stop or crash.
• Camera gimbals and phone stabilizer sensors cancel shakes by applying equal and opposite motions to make them more stable.
• Wearables/elevators detect sudden speed changes to trigger fall alerts or safety brakes.

Foundation for Newton’s Second Law

• Satellites mostly coast; small thrusters or reaction wheels act only to turn or correct the path.
• Games/VR assume motion stays the same until a coded force changes it.

Common misconceptions in inertia and motion

Newton’s laws of motion are easy; however, we usually get confused by comparing them with Aristotle’s hypothesis. Some of the most common confusions and their clarification are given below. 

1. Inertia is a force: There is a general myth that inertia is a force. Inertia isn’t push or pull; it’s a property of matter. It gives us the information about how much an object resists changes in motion. More mass -> more inertia. Inertia doesn’t act itself; it just makes acceleration harder.
2. A force is needed to keep something moving: To maintain the motion, one should keep pushing it. A force is usually needed to change motion, not to maintain it. When there is no net force, an object keeps a steady speed in a straight line.
3. Heavier objects fall faster than lighter ones: As per Aristotle, the heavier mass of an object is responsible for faster fall. However, in the case of a vacuum, all objects accelerate equally when falling. On Earth, heavier things sometimes land first because air resistance slows lighter, fluffier objects more –not because gravity favors mass. Galileo’s experiments overturned the old view. 
4. If it’s at rest, no forces act on it: There is a myth that a resting object has zero forces. The reality is that it can have several forces that balance out (\(\sum F =0\)). A book sits still because the table’s normal force balances the book’s weight.
5. Inertia makes the moving forces slow down:  In reality, inertia favors no change. Things slow down because of friction and drag.

Summary/Key Takeaways

Newton’s First Law has helped humans to understand motion and force in a great way. Some of the key takeaways are:

• Inertia isn’t force – it’s how hard it is to change an object’s motion; more mass, more stubbornness.
• Balanced forces = no change; unbalanced forces are the only reason speed or direction shifts.
• Turning needs a force, even if speed stays the same (that inward pull is what curves the path).
• Adding all the forces gives the net force.
• Always try to draw a tiny free-body diagram before identifying the forces on the object.

FAQs

Q1: How does inertia explain the passenger’s motion in the case of a bus?
Before the brakes are applied: The bus and the passengers are all in a state of uniform motion, traveling at the same constant velocity.

Q2: What is friction?
The contact force between the ball and the ground opposes the ball’s motion. This resistance, known as rolling friction, arises from minor deformations in the surfaces of both the ball and the ground.

Q3: What is Air Resistance (Drag)?
The air surrounding the ball pushes against it, also opposing its motion. This effect is more significant for faster-moving objects

References

1. Halliday, D., Resnick, R. and Walker, J. (2014) Fundamental of Physics. 10th Edition, Wiley and Sons, New York.
2. Newton, Isaac, 1642-1727. Newton’s Principia : the Mathematical Principles of Natural Philosophy. New-York :Daniel Adee, 1846.
3. Aristotle. “Physics.” The Complete Works of Aristotle: The Revised Oxford Translation, Vol. 1, edited by Jonathan Barnes, Princeton University Press, 1984, pp. [Page range for Books IV-VIII]
4. Galilei, Galileo. Dialogues Concerning Two New Sciences. Translated by Henry Crew and Alfonso de Salvio. Dover Publications, 1954
5. https://www.geeksforgeeks.org/physics/newtons-first-law-of-motion/
6. https://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law
7. https://byjus.com/physics/newtons-laws-of-motion-first-law/
8. https://www.sciencefacts.net/newtons-first-law.html