Force is a vector

1. Every physical quantity is either a scalar quantity or a vector quantity.
2. A scalar has a size only, such as a mass of $5kg$, a time of $20s$ or an energy of $300J$.
3. A vector has a size and a direction, such as a displacement of $40m$ north or a velocity of $3m/s$ to the left.
4. Force is a vector, because a push or pull always acts in a particular direction.
5. A $20N$ push to the right has a completely different effect from a $20N$ push to the left, even though the magnitude is the same.
6. To describe a force fully, you must give its magnitude in newtons and its direction, such as "$600N$ downwards" or "$50N$ to the left".
7. Direction can be given in words (up, down, left, right, forwards, backwards) or by using positive and negative signs along a chosen line.
   1. If you choose to the right as positive, a $50N$ force to the left is written as $-50N$.

Drawing forces as arrows

1. A vector is shown on a diagram as an arrow.
2. The direction of the arrow shows the direction in which the force acts.
3. The length of the arrow shows the magnitude of the force, so a larger force is drawn with a longer arrow.
4. Two forces of equal size are drawn as arrows of equal length, even if they point in different directions.
5. The arrow is drawn starting from the point where the force acts on the object.
   1. The weight of an object is drawn from the middle of the object, pointing straight down.
   2. A push from a hand or a pull from a rope is drawn from the point where the hand or rope touches the object.
6. An arrow drawn to scale uses a fixed length for each newton, so the size of a force can be read off the diagram.
   1. With a scale of $1cm$ to $10N$, a $35N$ force is drawn as an arrow $3.5cm$ long.
   2. Every arrow on the same diagram must use the same scale, or the lengths cannot be compared.
7. Each arrow is labelled with the name of the force, and with its value when the value is known.

Free body diagrams

1. A free body diagram shows one object on its own, with an arrow for every force that acts on it.
2. The object is drawn as a simple shape, such as a box or a dot, because its detailed appearance does not matter.
3. The surroundings, such as the floor, the rope or the Earth, are not drawn, because only their forces on the object are needed.
4. Forces that the object exerts on other things are not included, because they act on those other objects.
5. To draw a free body diagram, work through the object's interactions one at a time.
   1. Start with weight, because every object near the Earth has a gravitational force pulling it straight down.
   2. Add a force for every surface, string, rope or fluid that touches the object.
   3. Check that each arrow points in the right direction and that larger forces have longer arrows.
   4. Label every arrow with the name of the force.
6. The forces that appear most often on free body diagrams act in predictable directions.
   1. Weight acts vertically downwards.
   2. The normal contact force acts at right angles to the surface, so it acts upwards from a flat floor.
   3. Friction, air resistance and drag act in the opposite direction to the motion, or to the attempted motion.
   4. Tension acts along a string or rope, pulling away from the object.
   5. Thrust or driving force acts in the direction in which an engine, a motor or a person pushes the object.
   6. Upthrust acts vertically upwards on an object in a liquid or gas.
7. In the free body diagram of the car, the vertical arrows for weight and normal contact force are the same length, while the forward thrust arrow is longer than the backward friction arrow.
8. Reading the arrows tells you which forces are larger, which is the first step in working out how the object will move.