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This lesson covers all three of Newton's laws of motion as required by the AQA GCSE Physics specification (4.5.6). Newton's laws describe how forces affect the motion of objects and are fundamental to understanding all aspects of mechanics. You must be able to state each law, explain it with examples, and apply it to calculations.
Newton's first law states:
An object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant (unbalanced) force.
Inertia is the tendency of an object to resist a change in its motion. An object with more mass has more inertia — it is harder to start moving, harder to stop, and harder to change direction.
Inertial mass is defined as the measure of how difficult it is to change the velocity of an object. It can be calculated using:
m = F / a
Exam Tip: Newton's first law is often misunderstood. It does NOT say "objects at rest stay at rest." It says objects at rest OR moving at constant velocity will continue to do so unless a resultant force acts. A moving object does not need a force to keep moving — it needs a force to change its motion.
Newton's second law states:
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.
The equation is:
F = m x a
Where:
| Relationship | Effect |
|---|---|
| Double the force (same mass) | Double the acceleration |
| Triple the force (same mass) | Triple the acceleration |
| Double the mass (same force) | Halve the acceleration |
| Triple the mass (same force) | Third of the acceleration |
Example 1: A resultant force of 600 N acts on a car of mass 1200 kg. What is the acceleration?
a = F / m a = 600 / 1200 a = 0.5 m/s^2
Example 2: A bicycle and rider have a combined mass of 80 kg. The cyclist accelerates at 1.5 m/s^2. What is the resultant force?
F = m x a F = 80 x 1.5 F = 120 N
Example 3: A force of 50 N causes an object to accelerate at 10 m/s^2. What is the mass of the object?
m = F / a m = 50 / 10 m = 5 kg
graph LR
subgraph "Newton’s Second Law"
F["Force (N)"] -->|"F = m x a"| A["Acceleration (m/s^2)"]
M["Mass (kg)"] -->|"Inversely proportional"| A
end
style F fill:#e74c3c,color:#fff
style M fill:#2980b9,color:#fff
style A fill:#27ae60,color:#fff
Exam Tip: When using F = m x a, the force MUST be the RESULTANT force, not just any individual force. If there are multiple forces acting on the object, calculate the resultant force first, then use that in the equation. This is a very common mistake.
A car of mass 1500 kg has a driving force of 4000 N and friction forces of 1000 N.
Step 1: Calculate the resultant force. Resultant = 4000 - 1000 = 3000 N forwards
Step 2: Calculate the acceleration. a = F / m = 3000 / 1500 = 2 m/s^2
A ball of mass 0.5 kg is dropped. Air resistance is negligible.
The only force is weight: W = m x g = 0.5 x 9.8 = 4.9 N downwards
a = F / m = 4.9 / 0.5 = 9.8 m/s^2 downwards
(This shows that all objects fall with the same acceleration in the absence of air resistance, regardless of mass.)
A box of mass 10 kg slides down a frictionless slope. The component of gravity along the slope is 30 N.
a = F / m = 30 / 10 = 3 m/s^2 down the slope
Newton's third law states:
When two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.
This is often stated as: "For every action, there is an equal and opposite reaction."
Newton's third law force pairs have these characteristics:
| Feature | Description |
|---|---|
| Equal magnitude | Both forces are the same size |
| Opposite direction | The forces act in opposite directions |
| Same type | Both forces are the same type (e.g. both gravitational, both contact) |
| Act on different objects | Each force acts on a DIFFERENT object |
| Act simultaneously | Both forces exist at the same time |
Exam Tip: The most common mistake with Newton's third law is identifying the wrong pair. The weight of a book (Earth pulls book down) and the normal force from the table (table pushes book up) are NOT a Newton's third law pair — they both act on the SAME object (the book). The correct pair for the weight is: Earth pulls book down, book pulls Earth up. Both are gravitational forces acting on different objects.
These are a Newton's third law pair — both gravitational, equal in size, opposite in direction, acting on different objects.
The normal force from the table on the book is a separate interaction.
The forward friction force from the ground is what propels you forwards.
This is how a rocket can accelerate in space — there is no need to push against air or ground.
graph TD
subgraph "Newton’s Third Law: Book on Table"
E["Earth"] -->|"Pulls book down (weight)"| B["Book"]
B -->|"Pulls Earth up (reaction)"| E
end
subgraph "Walking"
F["Foot"] -->|"Pushes ground backward"| G["Ground"]
G -->|"Pushes foot forward"| F
end
style E fill:#2c3e50,color:#fff
style B fill:#2980b9,color:#fff
style F fill:#e67e22,color:#fff
style G fill:#27ae60,color:#fff
Stopping distance is the total distance a vehicle travels from the moment the driver sees a hazard to the moment the vehicle stops.
Stopping distance = thinking distance + braking distance
Thinking distance is the distance the vehicle travels during the driver's reaction time (the time between seeing the hazard and applying the brakes).
Thinking distance = speed x reaction time
Factors that increase thinking distance:
Braking distance is the distance the vehicle travels after the brakes are applied until it stops.
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