What Is Forces? A Visual Guide for IGCSE Physics Students

Force is a push, a pull, or a twist that changes motion

Every interaction in physics reduces to a single idea: force changes the state of motion of an object. A stationary football stays still until someone kicks it. A moving car slows down because friction and air resistance oppose its motion. A door swings on its hinges because a hand applies a turning force at a distance from the pivot. The entire forces section of IGCSE Physics (0625) builds outward from this principle, and every equation, diagram, and exam question traces back to it.

Force is measured in newtons (N). One newton is the force required to give a 1 kg mass an acceleration of 1 m/s². That definition isn't arbitrary: it comes directly from Newton's second law, which we'll unpack shortly. But first, a snapshot of the essential facts.

Key facts

• SI unit of force: newton (N)
• Force is a vector: it has both magnitude and direction. Two forces of equal size can produce completely different effects if they point in different directions.
• Contact forces: friction, air resistance, tension, normal contact force. These require physical contact between objects.
• Non-contact forces: gravitational force, electrostatic force, magnetic force. These act across empty space.
• Weight vs mass: mass (kg) is the amount of matter in an object and does not change with location. Weight (N) is the gravitational force on that mass: W = mg, where g is the gravitational field strength (approximately 9.8 N/kg on Earth's surface, often rounded to 10 N/kg in IGCSE calculations).
• Resultant force: the single force that has the same effect as all forces acting on an object combined.
• Equilibrium: when the resultant force is zero, the object either stays at rest or continues at constant velocity.

Newton's three laws of motion

Isaac Newton published his three laws in 1687, and they remain the foundation of classical mechanics. Each law builds logically on the previous one, and together they explain everything from a ball rolling along a table to a satellite orbiting the Earth.

Newton's first law: inertia

An object remains at rest, or continues moving at constant velocity in a straight line, unless acted on by a resultant force. The critical word is "resultant." Forces can act on an object without changing its motion, provided those forces cancel out. A book lying on a table has two forces acting on it: gravity pulling it down and the normal contact force pushing it up. These are equal and opposite, so the resultant force is zero, and the book stays put.

Why does this matter? Because students often assume that a moving object must have a force acting on it. Newton's first law says the opposite. If an object moves at constant velocity, the resultant force on it is zero. A car cruising at 60 km/h on a flat road has its engine force exactly balanced by friction and air resistance. No net force, no acceleration.

Newton's second law: F = ma

The resultant force on an object equals its mass multiplied by its acceleration: F = ma. This is arguably the most important equation in the IGCSE Physics syllabus. It tells you three things at once. A larger force produces a larger acceleration. A larger mass, for the same force, produces a smaller acceleration. And the direction of acceleration is always the same as the direction of the resultant force.

The equation works in SI units: force in newtons, mass in kilograms, acceleration in metres per second squared. If any of these aren't in SI, convert first. That conversion step catches out many candidates in exams.

Newton's third law: action and reaction

If object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These two forces act on different objects, are of the same type, and are equal in magnitude. A common exam error is confusing a Newton's third law pair with two balanced forces on the same object. The book on a table is not a third-law example. The weight of the book (Earth pulling the book) and the gravitational pull of the book on the Earth: that's a third-law pair. The normal contact force of the table on the book and the normal contact force of the book on the table: that's another third-law pair. Neither pair involves two forces on the same object.

Types of forces

Each of these forces has a specific cause, and identifying that cause is what distinguishes a correct free-body diagram from an incorrect one. You should never draw a force arrow on a diagram unless you can name the object that exerts it.

Free-body diagrams: thinking visually about forces

A free-body diagram isolates a single object and shows all the forces acting on it as arrows. The arrow's length represents the force's magnitude. The arrow's direction shows where the force acts. Nothing else appears on the diagram: no other objects, no velocities, no accelerations. Just the object and its forces.

Consider a box being pushed across a rough floor at constant velocity. Four forces act on it:

• Weight (downward): the gravitational pull of the Earth
• Normal contact force (upward): the floor pushing back against the box
• Applied force (horizontal, in the direction of motion): the push from the person
• Friction (horizontal, opposing motion): the floor resisting the sliding

Because the box moves at constant velocity, the resultant force is zero. That means weight equals normal force (vertically) and applied force equals friction (horizontally). All four arrows balance. If the person pushes harder, the applied force exceeds friction, and the box accelerates: Newton's second law takes over.

Resultant force and applying F = ma

The resultant force is the vector sum of all forces acting on an object. For forces along the same line, add forces in one direction and subtract forces in the opposite direction. The sign of the result tells you the direction of acceleration.

Worked example 1: Horizontal resultant

A 1200 kg car has an engine force of 3000 N forwards and experiences friction and air resistance totalling 1200 N backwards. Find the resultant force and the car's acceleration.

1. Resultant force: F = 3000 - 1200 = 1800 N (forwards)
2. Acceleration: a = F / m = 1800 / 1200 = 1.5 m/s² (forwards)

The cause-and-effect chain is clear. The engine force exceeds the resistive forces, so there is a net forward force. That net force, divided by the car's mass, produces a forward acceleration. If the driver lifts off the accelerator and the engine force drops to 1200 N, the resultant becomes zero and the car cruises at constant velocity. If the engine force drops below 1200 N, the resultant is negative (backwards), and the car decelerates.

Worked example 2: Vertical resultant

A 60 kg skydiver has just jumped from a plane. At this instant, her speed is low, so air resistance is negligible. Find her acceleration. Take g = 10 N/kg.

1. Weight: W = mg = 60 x 10 = 600 N (downward)
2. Air resistance: approximately 0 N (she's barely moving)
3. Resultant force: 600 N (downward)
4. Acceleration: a = F / m = 600 / 60 = 10 m/s² (downward)

At this instant, her acceleration equals g. That changes rapidly as she picks up speed, which leads directly to the concept of terminal velocity.

Terminal velocity: when forces balance during falling

As a falling object speeds up, air resistance increases. Weight stays constant (assuming the object doesn't lose mass), but drag grows with speed. At some point, air resistance equals weight. The resultant force drops to zero, acceleration stops, and the object falls at a constant speed called terminal velocity.

The logical sequence matters here, because exam questions frequently ask candidates to describe the motion of a falling object from the moment it's released:

1. Initially, speed is zero. Air resistance is zero. The only force is weight, so the object accelerates at g (approximately 10 m/s²).
2. As speed increases, air resistance increases. The resultant downward force decreases. The object still accelerates, but more slowly.
3. Eventually, air resistance equals weight. Resultant force is zero. Acceleration is zero. The object has reached terminal velocity.

A parachutist opening their parachute dramatically increases their cross-sectional area. Air resistance suddenly exceeds weight, creating an upward resultant. The parachutist decelerates. As speed drops, air resistance decreases until it once again equals weight, and a new, lower terminal velocity is reached. The entire sequence is a direct application of Newton's second law: whenever forces are unbalanced, the object accelerates in the direction of the resultant.

Momentum: the quantity of motion

Momentum measures how much motion an object has. It's defined as the product of mass and velocity: p = mv, measured in kg m/s. Momentum is a vector: its direction matches the velocity.

The principle of conservation of momentum states that the total momentum of a system remains constant, provided no external resultant force acts. This principle applies to collisions and explosions, and it's one of the most powerful tools in the IGCSE Physics toolkit.

Worked example 3: Collision

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. After the collision, they stick together and move off as one. Find the velocity after the collision.

1. Total momentum before: p = (2 x 3) + (1 x 0) = 6 kg m/s
2. Total mass after: 2 + 1 = 3 kg
3. By conservation of momentum: 6 = 3 x v
4. v = 6 / 3 = 2 m/s (in the original direction of motion)

The momentum before equals the momentum after. The speed decreased because the same momentum is now spread across a larger mass. That's the logic of conservation: momentum doesn't appear or disappear, it transfers between objects.

Worked example 4: Explosion

A 5 kg trolley at rest explodes into two pieces. One piece (mass 2 kg) flies off to the right at 4 m/s. Find the velocity of the other piece.

1. Total momentum before: 0 kg m/s (at rest)
2. Momentum of 2 kg piece: 2 x 4 = 8 kg m/s (rightward)
3. By conservation: 0 = 8 + (3 x v)
4. 3v = -8
5. v = -2.67 m/s (the negative sign means leftward)

The pieces fly in opposite directions, and the heavier piece moves more slowly. Total momentum remains zero, just as it was before the explosion.

Impulse: force multiplied by time

Newton's second law can be rewritten in terms of momentum. The resultant force equals the rate of change of momentum: F = (mv - mu) / t, where mu is the initial momentum and mv is the final momentum. Rearranging gives Ft = mv - mu. The quantity Ft is called the impulse, and it equals the change in momentum.

This relationship explains why car safety features work. In a crash, the change in momentum is fixed by the initial speed and the car's mass. A seatbelt and crumple zone increase the time over which the momentum changes. Because Ft = constant, increasing t reduces F. A smaller force on the passenger means less severe injuries. The same principle applies to catching a cricket ball: you move your hands backwards with the ball to extend the stopping time, reducing the force on your hands.

Worked example 5: Impulse and force

A 0.15 kg cricket ball travelling at 30 m/s is caught by a fielder who brings it to rest in 0.1 s. Calculate the average force exerted on the ball.

1. Change in momentum: mv - mu = (0.15 x 0) - (0.15 x 30) = -4.5 kg m/s
2. Force: F = (mv - mu) / t = -4.5 / 0.1 = -45 N
3. The magnitude of the force is 45 N. The negative sign indicates the force opposes the ball's original direction.

If the fielder stopped the ball in 0.01 s instead, the force would be 450 N: ten times larger. Extending the contact time is the entire engineering principle behind airbags, crash mats, and padded helmets.

Turning effects: moments and equilibrium

Forces don't just cause linear acceleration. A force applied at a distance from a pivot creates a turning effect, called a moment. The moment of a force is defined as:

Moment = force x perpendicular distance from the pivot

The unit is newton-metres (N m). "Perpendicular distance" means the shortest distance from the pivot to the line of action of the force. If the force isn't applied at right angles, you need the component of the distance that is perpendicular.

The principle of moments states that for an object in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point. This is the physical basis of every balance, lever, seesaw, and crane.

Worked example 6: The balanced beam

A uniform beam of length 4 m and weight 200 N is supported at its centre. A 300 N weight is placed 0.5 m from the left end. Where must a 150 N weight be placed to balance the beam?

1. The pivot is at the centre (2 m from each end). The beam is uniform, so its weight acts at the centre and creates no moment about the pivot.
2. The 300 N weight is 0.5 m from the left end, which is 1.5 m to the left of the pivot.
3. Clockwise moment (300 N weight): 300 x 1.5 = 450 N m
4. For balance, anticlockwise moment must equal 450 N m.
5. 150 x d = 450
6. d = 3.0 m from the pivot (to the right)

The lighter weight must be placed further from the pivot to produce the same moment. This is the principle behind using a long spanner to undo a tight bolt: the longer the distance, the greater the turning effect for the same force.

Conditions for equilibrium

An object is in complete equilibrium when two conditions are met simultaneously:

1. The resultant force in every direction is zero (no linear acceleration).
2. The resultant moment about any point is zero (no rotational acceleration).

A ladder leaning against a wall, a crane lifting a load, a bridge supporting traffic: each can be analysed by checking both conditions. If the forces balance but the moments don't, the object will rotate. If the moments balance but the forces don't, the object will accelerate linearly. Both must be satisfied for static equilibrium.

Key equations at a glance

Common mistakes and how to avoid them

Self-check questions

Work through each problem completely before checking the answer below.

1. A resultant force of 450 N acts on a 150 kg go-kart. Calculate the acceleration.
2. A skydiver of mass 70 kg reaches terminal velocity. State the size of the air resistance acting on her. Take g = 10 N/kg.
3. A 0.5 kg ball moving at 8 m/s hits a wall and bounces back at 6 m/s. Calculate the change in momentum. (Hint: assign a direction as positive.)
4. A uniform metre rule is balanced at the 50 cm mark. A 2 N weight hangs at the 15 cm mark. Where must a 1 N weight be placed to balance the rule?
5. Explain, using the idea of impulse, why a gymnast bends their knees when landing from a height.

Exam strategy for forces

Forces questions on the Cambridge IGCSE Physics papers test your ability to connect concepts, not just recall equations. A question about terminal velocity is really a question about Newton's second law applied to changing air resistance. A question about car safety is really a question about impulse and the force-time relationship. Recognising these connections is what separates a strong answer from a mediocre one.

Always start with a free-body diagram, even when the question doesn't ask for one. It organises your thinking and often reveals the solution before you write a single equation. Label every force, state its direction, and identify the resultant. From there, F = ma or the principle of moments will usually take you to the answer.

For extended-response questions worth 4 to 6 marks, examiners expect a logical chain of reasoning. Don't just state the answer. Walk through each step: identify the forces, determine the resultant, apply the relevant law, and state the consequence. Each link in that chain earns a mark. Skip a link and you lose it.