What Are Newton's Laws?
In 1687, Isaac Newton published Philosophiæ Naturalis Principia Mathematica — one of the most influential scientific works ever written. In it, he stated three laws of motion that, for more than two centuries, provided a complete description of how everything in the universe moves.
These three laws aren't arbitrary rules memorised for exams. They are precise, experimentally verified descriptions of how objects respond to forces. Understand them deeply and you can predict the trajectory of a thrown ball, the orbit of a satellite, the tension in a bridge cable, and the recoil of a rifle — using the same underlying principles.
Newton's laws apply in inertial reference frames — frames that are not accelerating. In everyday situations on Earth's surface (and ignoring Earth's rotation), this is an excellent approximation.
First Law: The Law of Inertia
An object remains at rest, or in uniform motion in a straight line, unless acted upon by an external net force.
Equivalently: if the net force on an object is zero, its velocity (both magnitude and direction) does not change.
Before Newton, the dominant view (inherited from Aristotle) was that objects naturally come to rest — that motion requires a continuous cause. Newton overturned this completely. The natural state is not rest, but constant velocity (which includes zero velocity as a special case).
The property of matter that resists changes in velocity is called inertia. More massive objects have more inertia — they are harder to accelerate from rest, harder to stop when moving, and harder to redirect.
Everyday Examples
- A hockey puck sliding on frictionless ice continues at constant speed in a straight line — no force, no change in velocity.
- You lurch forward when a car brakes suddenly. Your body wants to maintain its forward velocity; the seatbelt applies the force to change it.
- A spacecraft in deep space (negligible gravity, no air resistance) continues at constant velocity indefinitely without any thrust.
Second Law: F = ma
The net force on an object equals its mass times its acceleration.
In vector form: Fnet = ma
This is the most useful of the three laws — it's the equation of motion. Given the forces on an object and its mass, you can compute its acceleration, and from that, predict its entire future trajectory.
Several points are crucial:
- F is the net force — the vector sum of all forces acting on the object. A 10 N force right and a 10 N force left give zero net force, zero acceleration.
- Both F and a are vectors — they have both magnitude and direction. Acceleration always points in the same direction as the net force.
- Mass is the proportionality constant — doubling the mass halves the acceleration for the same force. This is why a truck accelerates more slowly than a bicycle under the same engine force.
Third Law: Action and Reaction
For every action there is an equal and opposite reaction.
More precisely: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces are equal in magnitude, opposite in direction, and act on different objects.
The third law is almost universally misunderstood. The key point is that action-reaction pairs always act on different objects. They can never cancel each other out — forces only cancel when they act on the same object.
"If every action has an equal and opposite reaction, how does anything ever accelerate?" — Because the paired forces act on different objects. The net force on each individual object is what matters for that object's acceleration.
Examples of Newton's Third Law
- Rocket propulsion: The rocket pushes exhaust gases backward; the gases push the rocket forward. The rocket accelerates because the rocket-gas reaction force acts on the rocket, not on the gas.
- Walking: Your foot pushes backward on the ground; the ground pushes forward on you. You accelerate forward because the ground's force acts on you.
- Swimming: Your hand pushes water backward; the water pushes you forward.
- A book on a table: Gravity pulls the book down (Earth on book). The table pushes the book up (normal force). These are NOT a Newton's third law pair — they act on the same object. The third law pair of gravity is the book pulling Earth upward.
More Worked Examples
Common Misconceptions
- "A moving object has a force on it." — No. A moving object in the absence of forces continues at constant velocity (First Law). Force is needed to change velocity, not to maintain it.
- "Heavier objects fall faster." — No. Ignoring air resistance, all objects fall with the same acceleration g regardless of mass. Although F = mg is larger for heavy objects, so is the resistance to acceleration (m), and they cancel exactly.
- "The normal force and gravity are a Newton's Third Law pair." — No. They act on the same object. The true third-law pair of gravity (Earth pulling you down) is you pulling Earth upward with equal force.
- "Newton's laws always apply." — They break down at very high speeds (need Special Relativity) and at atomic scales (need Quantum Mechanics). For everyday objects at everyday speeds, they are extraordinarily accurate.
Practice Problems
Test your understanding with these problems. Try each one before revealing the answer.
Reveal Solution ▼
Now that you understand Newton's laws, the natural next topics are Projectile Motion (applying the laws in 2D) and SUVAT equations (kinematics toolbox built on these laws).