Newton's Laws of Motion

Learning Objectives

State Newton's three laws of motion.

Define inertia, force, mass, and acceleration and describe their relationships.

Apply Newton's Second Law (F=ma) to solve basic dynamics problems.

Explain the concept of action-reaction pairs as described by Newton's Third Law.

The Foundation of Classical Mechanics

Sir Isaac Newton's three laws of motion form the basis of classical mechanics, describing the relationship between the motion of an object and the forces acting upon it.

Newton's First Law: The Law of Inertia

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

This law introduces the concept of inertia, which is the tendency of an object to resist changes in its state of motion. Mass (m) is a quantitative measure of inertia. An object with more mass has more inertia. The first law applies when the net force on an object is zero.

Newton's Second Law: Force and Acceleration

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force.

This is most famously expressed by the equation:

F_net = ma

Where:

F_net is the net force, the vector sum of all forces acting on the object (measured in Newtons, N).

m is the mass of the object (in kilograms, kg).

a is the acceleration of the object (in meters per second squared, m/s²).

This law is the cornerstone of dynamics. If you know the forces on an object, you can calculate its acceleration, and thus predict its future motion.

Example: A 10 kg box is pushed with a force of 50 N. Ignoring friction, what is its acceleration?

a = F/m = 50 N / 10 kg = 5 m/s².

Newton's Third Law: Action and Reaction

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

This means that forces always occur in pairs. If Object A exerts a force on Object B, then Object B simultaneously exerts a force on Object A that is equal in magnitude and opposite in direction.

Important points about action-reaction pairs:

The two forces act on different objects.

They are equal in magnitude and opposite in direction.

They are of the same type (e.g., both are gravitational forces, or both are contact forces).

A classic example is a rocket. The rocket expels hot gas downwards (action). The gas, in turn, pushes the rocket upwards (reaction). The force on the gas is equal and opposite to the force on the rocket.

Key Terms

Inertia: The property of an object to resist any change in its state of motion. Mass is the measure of inertia.
Force: An influence that can change the motion of an object. It is a vector quantity, having both magnitude and direction. The SI unit is the Newton (N).
Newton's Second Law: The fundamental law of motion stating that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass (F=ma).
Newton's Third Law: The law stating that for every action, there is an equal and opposite reaction