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Physics Fundamentals

Newton’s Laws of Motion

Learn how forces affect motion through Newton’s three laws, essential formulas, simple examples, and everyday applications.

Why does a passenger move forward when a car suddenly stops? Why does a rocket move upward when it pushes gases downward? Newton’s Laws of Motion help us answer questions like these. They describe the relationship between force, mass, and motion.

Definition: Newton’s Laws of Motion are three basic principles that explain how an object’s motion changes when forces act on it. They apply to many ordinary situations, from riding a bicycle to launching a spacecraft.

Before Learning the Laws: Important Ideas

Motion

Motion is a change in an object’s position over time compared with a reference point.

Force

A force is a push or pull. Force has both size and direction, so it is a vector quantity. Its SI unit is the newton (N).

Acceleration

Acceleration is the rate at which velocity changes. An object accelerates when it speeds up, slows down, or changes direction.

Balanced and Unbalanced Forces

Several forces may act on an object at the same time. The combined effect of all these forces is called the net force.

Balanced forces: The net force is zero. The object remains at rest or continues moving at constant velocity.
Unbalanced forces: The net force is not zero. The object accelerates in the direction of the net force.

F_net = ΣFF_net is the net force; ΣF means the vector sum of all forces.

Newton’s First Law: The Law of Inertia

An object keeps its state of motion unless an unbalanced external force acts on it.

An object at rest tends to remain at rest. An object moving with constant velocity tends to continue moving in a straight line at constant speed. This continues until a net external force changes its motion.

Inertia is an object’s tendency to resist a change in its motion. Greater mass means greater inertia. For example, it is harder to start or stop a heavy shopping cart than an empty one.

Everyday Example: A Sudden Stop

When a moving car stops suddenly, the car stops because the brakes provide an external force. However, passengers tend to continue moving forward because of inertia. A seat belt provides a force that helps change their motion safely.

Remember: Newton’s First Law does not say that a force is needed to keep an object moving at constant velocity. A force is needed to change velocity, not to maintain constant velocity in an ideal situation with no net force.

Newton’s Second Law: Force, Mass, and Acceleration

The acceleration of an object depends on the net force acting on it and its mass.

For a constant-mass object, a greater net force produces greater acceleration. For the same net force, a larger mass produces less acceleration.

F_net = maF_net = net force in newtons (N), m = mass in kilograms (kg), a = acceleration in metres per second squared (m/s²).

The formula can also be rearranged:

a = F_net ÷ m and m = F_net ÷ a

Understanding the Units

One newton is the force needed to give a mass of one kilogram an acceleration of one metre per second squared.

1 N = 1 kg·m/s²

Numerical Example: Finding Acceleration

A horizontal net force of 24 N acts on a box with a mass of 6 kg. What is the box’s acceleration?

Step 1: Write the formula
F_net = ma, so a = F_net ÷ m

Step 2: Substitute the values
a = 24 N ÷ 6 kg

Step 3: Calculate
a = 4 m/s²

The box accelerates at 4 m/s² in the direction of the net force.

Forces Commonly Used in Problems

Force	Meaning	Typical direction
Weight	The gravitational force acting on an object.	Downward, toward the attracting body.
Normal force	Support force exerted by a surface.	Perpendicular to the surface.
Friction	Force that opposes relative motion or attempted motion between surfaces.	Usually opposite the motion or tendency to move.
Tension	Pulling force transmitted through a stretched rope, cable, or string.	Along the rope or cable.
Air resistance	Force caused by air opposing an object’s motion.	Usually opposite the direction of motion.

Mass and Weight Are Not the Same

Mass measures the amount of matter in an object and is measured in kilograms. Weight is a force caused by gravity and is measured in newtons.

W = mgW = weight in newtons (N), m = mass in kilograms (kg), g = gravitational field strength in m/s².

Near Earth’s surface, gravitational acceleration is approximately 9.8 m/s². An object’s mass stays the same when it moves to another world, but its weight can change because the gravitational field strength changes.

Newton’s Third Law: Action and Reaction

When one object exerts a force on another object, the second object exerts an equal and opposite force on the first.

Forces always occur in pairs. The two forces have equal size and opposite directions, but they act on different objects.

F_{A on B} = −F_{B on A}The minus sign shows that the two forces point in opposite directions.

Examples of Newton’s Third Law

When you push against the floor while walking, the floor pushes you forward.
A swimmer pushes water backward, and the water pushes the swimmer forward.
A rocket pushes exhaust gases downward, and the gases exert an upward force on the rocket.
When a book pushes down on a table, the table pushes upward on the book.

Common misconception: The action and reaction forces do not cancel each other because they act on different objects. To find the net force on one object, include only forces acting on that object.

How to Solve Newton’s Laws Problems

Identify the object or system you are studying.
List all external forces acting on it.
Choose a positive direction, such as right or upward.
Find the net force by adding forces with signs according to their directions.
Use Newton’s Second Law: F_net = ma.
Check the units and direction of your answer.

Common Mistakes to Avoid

Confusing force with motion

An object can move with constant velocity even when the net force is zero. Force causes a change in velocity.

Ignoring net force

When several forces act, do not use just one force in F = ma. First calculate the total or net force.

Mixing up mass and weight

Mass is measured in kilograms. Weight is a force measured in newtons and is calculated using W = mg.

Exam tip: Draw a simple free-body diagram when a problem includes several forces. Use arrows to show each force and label its direction. This makes the net force easier to calculate.

Quick Recap

Newton’s Laws in One Minute

First Law: An object resists changes in motion. Zero net force means constant velocity.
Second Law: Net force, mass, and acceleration are related by F_net = ma.
Third Law: Forces come in equal and opposite pairs acting on different objects.
Force unit: The newton, where 1 N = 1 kg·m/s².
Weight formula: W = mg.
Always consider the net force, the object’s mass, and the direction of acceleration.