Scalars and vectors

A scalar has size only (mass, distance, speed, energy). A vector has size and direction (force, weight, velocity, displacement, acceleration, momentum).

A force is a push or a pull on an object that results from its interaction with another object. Because it has a direction, a force is always a vector — we draw it as an arrow whose length shows the size.

Tip: if a quantity needs the word "north", "up", "to the right" to make sense, it's a vector. If just a number-and-unit is enough, it's a scalar.

Scalar or vector?

Tap whether each quantity is a scalar (size only) or a vector (size + direction).

Two families of force

Some forces only act when objects touch; others act at a distance through a field:

• Contact forces — the objects are touching: friction, air resistance, tension, normal contact.
• Non-contact forces — act through a field with no touching: gravitational, magnetic, electrostatic.

Contact or non-contact?

Tap a force, then tap the box it belongs in.

Weight

Weight is the force of gravity on an object. It depends on the object's mass and the gravitational field strength, g:

On Earth g ≈ 9.8 N/kg. Weight is a vector that always acts straight down, as though all the object's mass were concentrated at one point — its centre of mass.

Don't confuse mass with weight. Mass (kg) is the amount of matter in an object and does not change with location. Weight (N) is the force of gravity on that mass, so it changes with location: an astronaut's mass is the same on the Moon, but their weight is about 1/6 of its Earth value because the Moon's g is smaller.

Your turn — weight

Free-body diagrams & the resultant

Usually several forces act on an object at once. A free-body diagram shows the object on its own with every force drawn as an arrow from it — the longer the arrow, the bigger the force. The single force with the same effect as all of them together is the resultant force.

Higher tier: a single force can be resolved into two forces (components) acting at right angles — and forces that act at an angle can be added tip-to-tail using a scale drawing to find the resultant.

Reading the diagram

Are there no forces on the stuck car?

Why won't the spring spring back?

Work done

When a force moves an object along the line of the force, it does work — transferring energy:

One joule is the work done when a force of 1 newton moves an object 1 metre (1 J = 1 N·m). Work done against friction is transferred to the thermal store — the surfaces get warmer.

Your turn — work done

Forces & elasticity — Hooke's law

For a spring, the extension is proportional to the force applied, up to the limit of proportionality:

The spring constant k measures stiffness. If the spring returns to its original length when the force is removed, the deformation was elastic; if it stays stretched, it was inelastic.

Elastic potential energy stored in a stretched spring is E_e = ½ k e². Required practical: hang masses on a spring and plot force against extension.

Your turn — Hooke's law

Why won't the spring spring back?

Why does a longer spanner work better?

Moments, levers & gears

A force can turn an object about a pivot. The turning effect is the moment, and it depends on the force and how far from the pivot it acts:

This is the principle of moments: when balanced, the total clockwise moment equals the total anticlockwise moment. Levers and gears use a long distance to multiply the effect of a force.

Think of a spanner. A long-handled spanner loosens a stiff bolt far more easily than a short one, even with the same push — because the moment is force × distance, so a longer handle (bigger d) gives a bigger turning effect for the same force.

Your turn — moment

Why does a longer spanner work better?

Pressure

A fluid (liquid or gas) pushes on every surface it touches. The pressure is the force spread over the area:

Higher tier: in a column of liquid the pressure increases with depth, density and gravity:

Floating & sinking: a submerged object feels greater pressure on its bottom than its top, giving an upthrust. A floating object has upthrust = weight; if the upthrust is still less than the weight when it is fully submerged, it sinks. Atmospheric pressure falls as you go higher, because there is less air above you pressing down.

Diving deeper

How can one line tell the whole journey?

Describing motion

• Distance is a scalar; displacement (distance in a straight line, with direction) is a vector.
• Speed is a scalar; velocity is speed in a given direction (a vector).
• Typical speeds: walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s.

Acceleration is how quickly velocity changes:

Equation sheet: for uniform acceleration, v² − u² = 2 a s (final² − initial² = 2 × acceleration × distance).

Your turn — acceleration

Velocity–time graphs

On a distance–time graph the gradient is the speed. On a velocity–time graph the gradient is the acceleration and (higher tier) the area under the line is the distance travelled.

Your turn — read the graph

How can one line tell the whole journey?

Why does a distracted driver stop later?

Newton's three laws

• First law: if the resultant force is zero, a still object stays still and a moving object keeps a constant velocity. The tendency to resist a change in motion is inertia.
• Second law: a resultant force makes an object accelerate — F = m a.
• Third law: when two objects interact, they exert equal and opposite forces on each other (an action–reaction pair).

Biggest misconception: a moving object does not need a resultant force to keep moving. By Newton's first law, with zero resultant force it carries on at a constant velocity forever. A force is only needed to change motion (speed up, slow down or turn) — not to maintain it. Things on Earth slow down only because friction and drag provide a resultant force.

Inertia is like a loaded shopping trolley. A full trolley (large mass) is much harder to get moving — and once moving, much harder to stop or steer — than an empty one. More mass means more inertia: a greater resistance to any change in motion.

Action–reaction pairs act on different objects, so they never cancel. Push off a wall on a skateboard: you push the wall (action) and the wall pushes you back (reaction). The two forces are equal and opposite but act on different bodies — the force on you is what sends you rolling away.

Your turn — Newton's second law

Stopping a car

Stopping distance = thinking distance + braking distance. Thinking distance is travelled during the driver's reaction time; braking distance is travelled once the brakes are applied.

• Thinking distance increases with speed and a longer reaction time (tiredness, alcohol, drugs, distractions).
• Braking distance increases with speed, and with poor road, tyre or brake conditions (wet, icy, worn).

Why does a distracted driver stop later?

Terminal velocity

A falling object speeds up until the upward air resistance grows to balance its downward weight. With the forces balanced the resultant force is zero, so it stops accelerating and falls at a steady maximum speed — its terminal velocity.

Terminal velocity ≠ no forces. At terminal velocity the resultant force is zero (so acceleration is zero), but weight and air resistance are both still acting — they simply balance. Opening a parachute hugely increases air resistance, so it briefly exceeds weight, the skydiver decelerates, and they settle to a new, slower terminal velocity.

What affects stopping?

Momentum

A moving object has momentum — a vector that depends on mass and velocity:

In a closed system (no outside forces), total momentum is conserved: the total momentum before an event equals the total momentum after it.

Physics only: force equals the rate of change of momentum, F = m Δv ÷ Δt. Spreading a collision over a longer time (crumple zones, air bags) reduces the force.

Your turn — momentum

The equations to know

You've covered the key ideas in AQA 4.5 — scalars & vectors, contact & non-contact forces, work, elasticity, moments, pressure, motion, Newton's laws, stopping distance and momentum. Press Finish to see your score.