Table of Contents
Introduction and Historical Background of Newton’s Law
Sir Isaac Newton, one of the most influential scientists in history, laid the groundwork for classical mechanics through his formulation of the three fundamental laws of motion. Born in 1643 in England, Newton’s contributions extended far beyond mechanics, touching mathematics, optics, and astronomy. However, his laws of motion, articulated in his seminal work Philosophiæ Naturalis Principia Mathematica (1687), remain the cornerstone of physics.
Before Newton, scientists like Galileo Galilei and Johannes Kepler had made significant observations about motion. Galileo’s experiments on inclined planes revealed that objects accelerate uniformly under gravity and continue moving unless acted upon by an external force. Building on such insights, Newton formulated laws that explained the relationship between force, mass, and motion in a systematic way.
Newton’s law not only unified the understanding of motion but also provided a framework for predicting the behavior of objects in both terrestrial and celestial contexts. They remain critical in engineering, astronomy, and everyday phenomena.
Newton’s Three Laws of Motion and Key Experiments
1. First Law of Motion (Law of Inertia)
First Law of Motion Statement and explanation
Every object perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
The Newton’s first law reported above express the principle of inertia. An object remains at rest, or in uniform motion in a straight line, unless acted upon by an external force.
The tendency of objects to resist changes in their state of motion. Essentially, if no net force acts on an object, it will continue moving at a constant velocity or remain stationary.
This statement introduces also the concept of inertial observer. Imagine you are sitting in a train, and another train is stopped on the parallel line. At a certain point seems that the other train starts moving. But, in reality it is the train where we are sitting that is moving and we understand this looking to the ground and seeing that we are going far from an object that we know is static (e.g. the station or the platform).
The illusion of motion occurs because your body is used to your train being at rest, so when it accelerates slowly, your inertia makes it feel like the other train is moving.
This shows how inertia explains both actual motion and our perception of motion. It’s a perfect real-world demonstration of the first law: an object’s state of motion doesn’t change unless a force acts on it.
Galileo and the Inclined Plane
Before Newton, Galileo Galilei studied how objects move and laid the groundwork for the concept of inertia. He noticed that objects do not naturally “stop” unless something interferes.
On the right a movie clip that has newton’s first law.
- Galileo rolled a ball down a sloped plane.
- He observed that the ball accelerated as it went downhill due to gravity.
- Then, he rolled the ball up another slope and noticed it slowed down.
- If he made the second slope less steep or flat, the ball rolled farther before stopping.
- He even imagined a perfectly frictionless horizontal plane: on such a surface, the ball would keep rolling forever without slowing down.
What It Shows
- The ball naturally resists changes to its motion — this resistance is called inertia.
- Friction and air resistance in the real world act as external forces that eventually stop the ball.
- In a world without external forces (frictionless surface), the ball would move in a straight line at a constant speed forever.
Connection to Newton’s First Law
- Newton formalized Galileo’s observation: an object stays at rest or in uniform motion unless acted upon by an external force.
- Galileo’s inclined plane experiments essentially demonstrate that motion does not require a continuous force, contrary to the old Aristotelian belief.
2. Second Law of Motion (Law of Acceleration)
Second Law of Motion Statement and explanation
The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically:
(1) 
Where F is force, m is mass, and a is acceleration.
This law quantifies the relationship between force, mass, and acceleration. A greater force produces greater acceleration, while a larger mass resists acceleration.
Classic Experiment: Dynamics Cart on a Track
Apparatus
- A low-friction dynamics cart
- A smooth horizontal track
- Weights or masses to vary force
- A pulley system
- A string connecting the cart to hanging weights
- Stopwatch or motion sensor
Procedure
- Place the cart on the track. Attach a string to the cart and pass it over a pulley at the end of the track.
- Hang a weight at the other end of the string. This weight provides the force acting on the cart.
- Release the system so the weight falls, pulling the cart along the track.
- Measure the acceleration of the cart.
- Repeat the experiment with:
- Different weights (changing the force F)
- Different carts or added masses (changing the mass m)
Observation and Conclusion
- Increasing the hanging weight (greater force) → greater acceleration of the cart.
- Increasing the mass of the cart while keeping the same hanging weight → smaller acceleration.
Therefore, this confirms Newton’s second law: Acceleration is directly proportional to the applied force and acceleration is inversely proportional to the mass of the object.
3. Third Law of Motion (Action and Reaction)
Third Newton’s Law of Motion Statement and explanation
To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
For every action, there is an equal and opposite reaction. This Newton’s law emphasizes the mutual interactions between objects. Whenever one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction on the first object.
In other words, if one body exerts a force on a second body, the second body is also exerting a force on the first body, of equal magnitude in the opposite direction. Overly brief paraphrases of the third law, like “action equals reaction” might have caused confusion among generations of students: the “action” and “reaction” apply to different bodies. For example, consider a book at rest on a table. The Earth’s gravity pulls down upon the book. The “reaction” to that “action” is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.
Experiment: Jumping off a Boat
Imagine you are standing on a small boat at a dock and you jump forward onto the pier.
- Action: You push backward on the boat with your legs.
- Reaction: The boat pushes you forward with an equal force, propelling you onto the pier.
This is why the boat often slides slightly backward when you jump off — even though your main motion is forward. The forces are equal in magnitude and opposite in direction. The action force acts on the boat (pushing it backward), while the reaction force acts on you (pushing you forward).
Examples of Newton’s Laws in Space
First Newton’s Law: An asteroid drifting in the vacuum of space (far from planets, starts and so on). Once it’s moving, it will keep moving in the same direction and at the same speed indefinitely because there is almost no air resistance or friction to slow it down. It only changes its motion if an external force acts on it, like a thruster firing or the gravity of a nearby planet pulling it.
Second Newton’s Law: when a rocket fires its thrusters, the force from the expelled gas pushes the spacecraft forward. The acceleration of the spacecraft depends on how strong the force is and the mass of the spacecraft. A heavier spacecraft accelerates less for the same force, while a lighter spacecraft accelerates more.
Thirst Newton’s Law: When a rocket engine expels gas out of its nozzles at high speed (action), the rocket is pushed in the opposite direction (reaction). This works in the vacuum of space because the rocket doesn’t need air to push against; the expelled gas itself provides the reaction force that moves the rocket forward.
The video on the left show examples of Newton’s Law of Motion.
Newton’s Law are the basic concepts needed to understand how objects move in space.
Key Takeaways on Newton’s Law of Motion
Newton’s law of motion transformed human understanding of the physical world. They provide a framework for explaining and predicting the behavior of objects under forces, bridging the gap between observation and mathematics. While modern physics has extended beyond Newton’s law in the realms of relativity and quantum mechanics, for everyday applications and classical mechanics, these laws remain fundamental, timeless, and indispensable.
Here are the key takeaways of Newton’s Laws of Motion:
- First Law (Inertia): Objects resist changes in motion; they stay at rest or move uniformly unless acted upon by a force.
- Second Law (F = ma): The acceleration of an object depends on the net force applied and its mass; more force → more acceleration.
- Third Law (Action-Reaction): Every force has an equal and opposite reaction; forces always come in pairs.
- Inertia is everywhere: Even if we don’t notice, friction and air resistance mask it in daily life.
- Mass vs. Weight: Mass is matter, weight is the gravitational force on that mass.
- Limits: Works for everyday speeds and sizes; breaks down at very high speeds or quantum scales.
FAQ: Newton’s Laws of Motion
1. What are Newton’s Laws of Motion?
Newton’s Laws of Motion are three fundamental principles that describe how objects move. They were formulated by Sir Isaac Newton in 1687.
- First Law (Law of Inertia): An object will stay at rest or continue moving at a constant velocity unless acted upon by a net external force.
- Second Law: The acceleration of an object depends on the force applied and its mass:
- Third Law: For every action, there is an equal and opposite reaction.
2. What is inertia?
Inertia is the tendency of an object to resist changes in its state of motion.
- Example: A stationary ball won’t move unless you push it. A rolling ball won’t stop immediately unless friction or another force acts on it.
3. How do I calculate force?
Using Newton’s Second Law:
- F = force (Newtons, N)
- m = mass (kg)
- a = acceleration (m/s²)
Example: A 5 kg object accelerates at 2 m/s². 
4. Can an object move without a force?
Yes, if it’s already moving at constant velocity in a frictionless environment.
Newton’s First Law says an object does not need a force to keep moving, only to change its velocity (speed or direction).
5. What does “action-reaction” mean?
Every force comes in pairs: if object A exerts a force on object B, object B exerts an equal and opposite force on object A.
- Example: When you jump, your legs push on the ground (action), and the ground pushes you upward (reaction).
6. Why don’t we notice inertia in daily life?
Because friction and air resistance act on almost everything, making forces visible as we stop, start, or slow objects. Without these forces, inertia would be very obvious—objects would keep moving indefinitely.
7. Are Newton’s Laws valid everywhere?
Newton’s Laws work extremely well for everyday objects and most engineering scenarios. However:
- They don’t apply at very high speeds (close to the speed of light) — special relativity is needed.
- They don’t work at quantum scales — quantum mechanics governs small particles.
8. Common mistakes to avoid
Ignoring friction, air resistance, or other forces when analyzing motion.
Confusing mass and weight. (Mass = amount of matter, Weight = force due to gravity.)
Thinking force is needed to keep an object moving.