Forces & Motion
Understand Newton's three laws of motion, how forces combine to produce a net force, what causes acceleration, and how friction affects movement in everyday situations.
What Is a Force?
A force is a push or pull acting on an object. Forces can change an object's speed, direction, or shape. Forces are measured in newtons (N) and are vector quantities — they have both a magnitude (size) and a direction.
When multiple forces act on an object, we can calculate the net force (resultant force) by adding forces acting in the same direction and subtracting forces acting in opposite directions.
Net Force Diagrams
Balanced (Net = 0 N)
Object stays still or moves at constant velocity
Unbalanced (Net = 20 N right)
Object accelerates to the right
Gravity = Normal force (Net = 0 N vertically)
Object rests on a surface
Common Types of Forces
Newton's Three Laws of Motion
Sir Isaac Newton (1643–1727) described three fundamental laws that explain how forces affect the motion of objects. These laws form the foundation of classical mechanics.
Newton's First Law — Law of Inertia
"An object at rest stays at rest, and an object in motion stays in motion at the same speed and in the same direction, unless acted on by an unbalanced (net) force."
In plain English: Objects do not change their motion on their own. You need a net force to start, stop, or change the direction of motion. This resistance to change is called inertia.
Examples: A ball rolling on a smooth surface keeps rolling. A passenger lurches forward when a bus brakes suddenly. A tablecloth pulled quickly leaves the dishes behind.
Newton's Second Law — Law of Acceleration
"The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."
Where F = net force (N), m = mass (kg), a = acceleration (m/s²).
Examples: A heavier trolley needs more force to accelerate. Doubling the net force doubles the acceleration. A car with a bigger engine accelerates faster for the same mass.
Newton's Third Law — Law of Action and Reaction
"For every action force, there is an equal and opposite reaction force."
Forces always act in pairs. If Object A exerts a force on Object B, then Object B exerts an equal force in the opposite direction on Object A. These forces act on different objects, so they do not cancel each other out.
Examples: Rocket engines push exhaust gas backward; the gas pushes the rocket forward. A swimmer pushes water backward with their hands; the water pushes the swimmer forward. A gun recoils when fired.
Friction and Acceleration
Friction is a force that opposes motion between surfaces that are in contact. It acts in the opposite direction to movement. The amount of friction depends on the roughness of the surfaces and the force pressing them together (normal force).
Friction Can Be Helpful
- Car tyres grip the road for steering and braking
- Shoes grip the ground for walking
- Screws stay in walls because of friction
- Matches ignite when struck (friction → heat)
Friction Can Be a Problem
- Wears down machine parts over time
- Wastes energy as heat in engines
- Slows moving vehicles down
- Reduced by lubrication (oil, grease) or smooth surfaces
Terminal Velocity
When an object falls, gravity accelerates it downward while air resistance acts upward. As the object speeds up, air resistance increases. Eventually, air resistance equals gravity — the forces are balanced, the net force is zero, and the object stops accelerating. It falls at a constant speed called terminal velocity. A skydiver reaches terminal velocity before opening their parachute. Opening the parachute greatly increases air resistance, reducing terminal velocity to a safe landing speed.
Key Vocabulary
Inertia
The tendency of an object to resist changes to its state of motion. Objects with greater mass have greater inertia and are harder to accelerate or stop.
Net Force
The overall (resultant) force acting on an object after all individual forces are added together as vectors. If net force is zero, forces are balanced.
Acceleration
The rate of change of velocity (m/s²). An object accelerates when there is an unbalanced net force. a = F/m (Newton's Second Law).
Terminal Velocity
The constant falling speed reached when air resistance equals gravitational force, so net force is zero and acceleration is zero.
Worked Examples
A 10 kg box is pushed with a force of 80 N. Friction acts with a force of 20 N. Calculate the acceleration of the box.
Step 1: Find net force. Forces act in opposite directions: Push = 80 N forward; Friction = 20 N backward.
Net force = 80 − 20 = 60 N forward
Step 2: Apply Newton's Second Law. a = F/m = 60 N ÷ 10 kg
Answer: a = 6 m/s² in the direction of the push.
A 60 kg person stands on a set of scales in a lift. The lift accelerates upward at 2 m/s². What force do the scales read?
Weight (downward) = mg = 60 × 10 = 600 N
Net upward force required for acceleration: F_net = ma = 60 × 2 = 120 N
The scale reads the normal force (N) = Weight + net upward force = 600 + 120 = 720 N
Answer: The scales read 720 N — the person "feels heavier" in an accelerating lift.
Explain Newton's Third Law using the example of a swimmer pushing against the pool wall.
Action: The swimmer's feet push backward against the wall with a force (say, 200 N).
Reaction: The wall pushes the swimmer's feet forward with an equal force of 200 N.
These forces are equal in magnitude and opposite in direction, but they act on different objects (feet push wall; wall pushes swimmer).
Result: The swimmer accelerates away from the wall. The wall does not move (Earth's mass is enormous).
Knowledge Check
Loading questions…
Key Concepts Summary
- ✓ A force is a push or pull measured in newtons (N). Forces can change speed, direction, or shape.
- ✓ Newton's 1st Law: Objects resist changes to their motion (inertia) unless a net force acts on them.
- ✓ Newton's 2nd Law: F = ma. Greater force or smaller mass means greater acceleration.
- ✓ Newton's 3rd Law: Every action has an equal and opposite reaction force, acting on different objects.
- ✓ Friction opposes motion; it can be helpful or harmful depending on the situation.
- ✓ Terminal velocity is reached when gravity equals air resistance, resulting in zero net force and constant speed.