Newton's Laws of Motion

This lesson covers Newton's three laws of motion — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to be able to state, explain, and apply each of the three laws to a variety of situations.

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Newton's First Law

Newton's First Law: An object will remain stationary or continue to move at a constant velocity unless acted upon by a resultant force.

What Does This Mean?

• If an object is stationary and no resultant force acts on it, it stays stationary.
• If an object is moving and no resultant force acts on it, it continues to move in a straight line at constant speed.
• A resultant force is needed to change an object's velocity — to make it speed up, slow down, or change direction.

Inertia

Inertia is the tendency of an object to resist a change in its state of motion. It is directly related to mass — the greater the mass, the greater the inertia, and the harder it is to change the object's motion.

• A bowling ball has a large mass and therefore large inertia — it is hard to get moving and hard to stop.
• A tennis ball has a small mass and therefore small inertia — it is easy to get moving and easy to stop.

Examples of Newton's First Law

Example 1: A book on a desk. The book is stationary. The weight (downward) and normal contact force (upward) are balanced. The resultant force is zero, so the book remains stationary.

Example 2: A hockey puck on ice. Once hit, the puck slides across the ice. If the ice were perfectly smooth (no friction), the puck would continue at constant velocity forever. In practice, a small friction force gradually slows it down.

Example 3: Passengers in a braking car. When a car brakes suddenly, the passengers continue to move forward (due to inertia) until a force (seatbelt) acts to decelerate them.

Exam Tip: Newton's First Law does NOT say "an object at rest stays at rest." It says an object remains at rest or at constant velocity. Many students forget the "constant velocity" part. An object moving at constant velocity has zero resultant force — this is a key concept.

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Newton's Second Law

Newton's Second Law: The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.

This is expressed as the equation:

force = mass × acceleration

$F = ma$F=ma

Where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

Rearrangements

• a = F ÷ m (acceleration = force ÷ mass)
• m = F ÷ a (mass = force ÷ acceleration)

What Does This Mean?

• The greater the force, the greater the acceleration (for a given mass).
• The greater the mass, the smaller the acceleration (for a given force).
• If the resultant force is zero, the acceleration is zero — the object moves at constant velocity (consistent with Newton's First Law).

Worked Examples

Example 1: A resultant force of 600 N acts on a car of mass 1200 kg. Calculate the acceleration.

a = F ÷ m = 600 ÷ 1200 = 0.5 m/s²

Example 2: A 0.15 kg ball accelerates at 20 m/s². What is the resultant force?

F = ma = 0.15 × 20 = 3.0 N

Example 3: A force of 50 N accelerates an object at 2 m/s². What is the object's mass?

m = F ÷ a = 50 ÷ 2 = 25 kg

Example 4: A car of mass 1500 kg has a driving force of 4500 N and friction of 1500 N. Calculate the acceleration.

Step 1: Find the resultant force. Resultant = 4500 − 1500 = 3000 N

Step 2: Apply F = ma. a = F ÷ m = 3000 ÷ 1500 = 2.0 m/s²

Exam Tip: Always use the resultant force in F = ma, not just any single force. If there are multiple forces, calculate the resultant first. This is the most common error on exam questions about Newton's Second Law.

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Newton's Third Law

Newton's Third Law: When two objects interact, they exert equal and opposite forces on each other.

Key Points About Newton's Third Law

The two forces in a Newton's Third Law pair:

1. Are equal in magnitude.
2. Act in opposite directions.
3. Act on different objects.
4. Are the same type of force.

Examples of Newton's Third Law

Example 1: A person standing on the floor.

• The person pushes down on the floor with a force (due to their weight).
• The floor pushes up on the person with an equal force (normal contact force).
• These forces are equal in size, opposite in direction, and act on different objects (one on the floor, one on the person).

Example 2: Earth and Moon.

• The Earth pulls the Moon toward it with gravitational force.
• The Moon pulls the Earth toward it with an equal gravitational force.
• Both forces are gravitational, equal in size, opposite in direction, and act on different objects.

Example 3: A swimmer pushing off a wall.

• The swimmer pushes the wall backward (contact force).
• The wall pushes the swimmer forward with an equal contact force.
• The swimmer accelerates because the force acts on the swimmer (low mass).
• The wall does not noticeably move because it is attached to the ground (very large mass).

graph LR
    A["Swimmer"] -- "Swimmer pushes wall →" --> B["Wall"]
    B -- "← Wall pushes swimmer" --> A

    style A fill:#2980b9,color:#fff
    style B fill:#2c3e50,color:#fff

A Common Misconception

"If the forces are equal and opposite, don't they cancel out?"

No. Newton's Third Law pairs act on different objects, so they cannot cancel. Forces only cancel (balance) when they act on the same object.

• Weight and normal contact force on a book are NOT a Newton's Third Law pair — they both act on the same object (the book). They happen to be equal and opposite when the book is in equilibrium, but they are different types of force.
• The Newton's Third Law pair of the weight of the book is: the Earth pulls the book down (gravity) and the book pulls the Earth up (gravity). These are the same type of force, equal in magnitude, opposite in direction, and act on different objects.