Newton's Laws of Motion

Newton's Three Laws of Motion

Isaac Newton published his three laws of motion in 1687. They remain the foundation of classical mechanics and describe how forces affect the motion of objects.

First Law — Law of Inertia

An object will remain at rest or continue moving in a straight line at constant speed unless acted upon by a resultant (unbalanced) force.

This means objects do not naturally slow down — they only stop because of forces like friction and air resistance. In the absence of forces (e.g., in deep space), an object would travel forever at constant velocity.

Inertia is the property of matter that causes it to resist changes in motion. A more massive object has greater inertia — it takes more force to start, stop, or change its direction.

Examples:

• A book on a table remains still (balanced forces — weight down equals normal force up)
• Passengers lurch forward when a bus brakes suddenly (inertia keeps them moving)
• A hockey puck on ice keeps sliding with little friction to slow it

Second Law

The acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.

Formula: F = ma

Where:

• F = resultant force (Newtons, N)
• m = mass (kilograms, kg)
• a = acceleration (metres per second squared, m/s squared)

Rearranged:

• a = F / m
• m = F / a

Implications:

• Double the force → double the acceleration
• Double the mass → half the acceleration (for the same force)

Third Law — Action and Reaction

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

Crucially, these forces act on different objects — they are not the same force and do not cancel each other out.

Examples:

• You push the floor down → the floor pushes you up (allowing you to walk)
• A rocket expels exhaust gas downward → the gas pushes the rocket upward
• Earth pulls you down (gravity) → you pull Earth upward with the same force (but Earth barely accelerates because it has enormous mass)
• A swimmer pushes water backward → the water pushes the swimmer forward

Worked Examples

Example 1 — Finding force: A 4 kg ball accelerates at 5 m/s squared. Find the resultant force. F = ma = 4 x 5 = 20 N

Example 2 — Finding acceleration: A 1200 kg car has a driving force of 3600 N and friction of 1200 N. Find the acceleration. Resultant force = 3600 - 1200 = 2400 N a = F / m = 2400 / 1200 = 2 m/s squared

Example 3 — Third Law pair: A horse pulls a cart with 500 N. By Newton's Third Law, the cart pulls the horse backward with 500 N. The horse and cart accelerate because the ground pushes the horse's hooves forward (another Third Law pair) with more force than friction resists.

Resultant Force

The resultant force is the single force that represents the combined effect of all forces acting on an object.

• Forces in the same direction add together
• Forces in opposite directions subtract

If resultant force = 0 N → the object is in equilibrium: stationary or moving at constant velocity (Newton's First Law)

If resultant force is not zero → the object accelerates in the direction of the resultant (Newton's Second Law)

Free Body Diagrams

A free body diagram shows all forces acting on an object:

• Each force is shown as an arrow
• The length of the arrow represents the magnitude of the force
• The direction of the arrow shows the direction of the force
• Label each arrow with the force name and magnitude

Common forces in free body diagrams:

• Weight (W) — downward, from the centre of mass
• Normal reaction (N) — perpendicular to the surface, upward for objects on flat surfaces
• Friction (f) — opposing direction of motion, horizontal
• Air resistance / drag (D) — opposing direction of motion
• Thrust / driving force (T) — in direction of motion

Terminal Velocity

When an object falls through air:

1. Initially, weight > air resistance → accelerates downward
2. As speed increases, air resistance increases
3. Eventually, air resistance = weight → resultant force = 0
4. Object falls at terminal velocity (constant speed)

A skydiver reaches terminal velocity at around 55 m/s in a spread position. Opening a parachute dramatically increases air resistance, reducing terminal velocity to a safe landing speed.

Key Terms

• Inertia — resistance to changes in motion; greater for more massive objects
• Resultant force — the net force after all forces are combined (with direction)
• Equilibrium — state where resultant force = 0; object is stationary or at constant velocity
• Terminal velocity — constant speed reached when driving force equals resistive force
• Free body diagram — diagram showing all forces on an object as labelled arrows

Common Mistakes

• Thinking Newton's Third Law pairs cancel out — they act on different objects so they do not cancel
• Saying an object at constant velocity has no forces — it has balanced forces (resultant = 0)
• Forgetting to calculate the resultant force before applying F = ma when multiple forces act
• Confusing weight (a force, in N) with mass (in kg) in the F = ma calculation

Tips and Tricks

• For F = ma, use the formula triangle: F on top, m and a on the bottom
• Always find the resultant force first (add/subtract forces) before using F = ma
• Third Law pairs: same size, opposite direction, different objects, same type of force
• Free body diagrams: if the arrow lengths are equal and opposite, the object is in equilibrium