Scalars, Vectors and Forces

Physical quantities in physics fall into two groups depending on whether direction matters.

A scalar quantity has magnitude (size) only. A vector quantity has both magnitude and direction.

Magnitude just means "how much" or "how big". Speed of 30 m/s is a magnitude. But velocity of 30 m/s due north is a magnitude and a direction, which makes it a vector.

Knowing the direction of a vector genuinely changes the physics. A 10 N force pushing a box left and a 10 N force pushing it right have the same magnitude but opposite effects, because they are vectors pointing in opposite directions. For a scalar such as mass, direction is meaningless: a 2 kg bag of sugar has no "direction".

Scalar quantities	Vector quantities
mass	force
speed	velocity
distance	displacement
energy	acceleration
temperature	weight
time	momentum

A vector is drawn as an arrow. The arrow carries both pieces of information at once.

The length of the arrow represents the magnitude of the vector. The direction the arrow points represents the direction of the vector.

So a long arrow means a large quantity and a short arrow means a small one, drawn to a consistent scale. Two forces can be compared just by looking: the longer arrow is the bigger force.

Consider a person pushing a trolley with a force of 40 N to the right while friction of 10 N acts to the left:

Push (40 N)        Friction (10 N)
─────────────────►      ◄─────

The push arrow is drawn four times longer than the friction arrow because it is four times bigger, and it points the opposite way. This drawing-to-scale idea is the foundation for adding forces together, which you meet when calculating resultant forces.

You feel forces constantly, but the physics definition is precise.

A force is a push or a pull on an object caused by an interaction with another object.

The key word is interaction: a force never exists on its own. There is always a second object involved. When you kick a ball, your foot (one object) interacts with the ball (another object). When Earth pulls on you, Earth is the second object.

Force is measured in newtons (N) and, crucially, force is a vector quantity. It has a size and a direction, so it is drawn as an arrow. Describing the size of a force without its direction leaves out half the information. Saying "a 5 N force" is incomplete for many exam questions; "a 5 N force acting downwards" is complete.

Forces are divided into two categories depending on whether the interacting objects are touching, covered on the next slides.

A contact force acts only when the two interacting objects are physically touching.

The moment the objects separate, a contact force disappears. Push a book across a table and friction acts; lift the book off the table and that friction vanishes because the surfaces no longer touch.

Contact forces you must be able to name: friction, air resistance, tension, and the normal contact force.

Contact force	What causes it	Everyday example
Friction	Two surfaces rubbing or sliding against each other	A box being dragged across the floor
Air resistance	A moving object pushing through air particles	A skydiver falling; a car at speed
Tension	A stretched rope, cable or string being pulled taut	A tug-of-war rope; a lift cable
Normal contact force	A surface pushing back on an object resting on it	A table pushing up on a laptop

The normal contact force always acts at right angles ("normal") to the surface. A book resting on a horizontal table experiences a normal contact force acting straight upwards.

A non-contact force acts between two objects that are not touching. The force acts across a gap, at a distance.

This can feel strange, because in everyday life pushing something usually means touching it. But a dropped ball accelerates towards the ground with nothing touching it, and two magnets repel before they meet. These forces act through fields.

Non-contact forces you must be able to name: gravitational force, electrostatic force, and magnetic force.

Non-contact force	What causes it	Everyday example
Gravitational force	The mass of objects attracting each other	Your weight; the Moon orbiting Earth
Electrostatic force	Objects carrying electric charge attracting or repelling	A charged balloon sticking to a wall
Magnetic force	Magnets and magnetic materials attracting or repelling	Two bar magnets pushing apart

A useful test: if you can separate the two objects and the force still acts across the gap, it is non-contact. Pull two magnets apart and they still tug on each other, so magnetism is non-contact.

Because a force is always an interaction between two objects, forces can be described as an interaction pair, with each object exerting a force on the other.

Take the Sun and Earth. The Sun's gravity pulls on Earth, and Earth's gravity pulls back on the Sun. This is a non-contact interaction pair, drawn as two force vectors pointing towards each other:

   Force on Earth          Force on Sun
◄──────────────  Earth    Sun  ──────────────►

A contact interaction pair works the same way. When you lean on a wall, you push on the wall and the wall pushes back on you with an equal force in the opposite direction.

In an interaction pair, the two forces act on different objects, are equal in size and act in opposite directions.

Being able to describe these pairs as vectors, and identify whether the interaction is contact or non-contact, is exactly what the specification asks for. You develop this idea further when you meet resultant forces and Newton's Third Law.

1. Calling speed and velocity the same thing

Speed is a scalar (magnitude only); velocity is a vector (magnitude and direction). The same trap applies to distance (scalar) versus displacement (vector). Marks are lost when the two are used interchangeably.

2. Forgetting that force is a vector

A force answer usually needs a direction as well as a size. "A resultant force of 20 N" is often incomplete; "a resultant force of 20 N to the right" is complete.

3. Mixing up contact and non-contact forces

Gravity, magnetism and electrostatic force act at a distance, so they are non-contact. Friction, tension, air resistance and the normal contact force need surfaces to touch, so they are contact forces. Learn the two lists.

4. Drawing vector arrows without regard to length

The length of a force arrow should match its magnitude. A 30 N force must be drawn longer than a 10 N force on the same diagram, or the diagram misrepresents the physics.

5. Thinking a single object can have a force "by itself"

Every force comes from an interaction with a second object. If you cannot name what is producing the push or pull, you have not identified the force correctly.