Vectors and Scalars

Scalars are simple - they're just magnitudes (sizes) without any direction. Think of distance: if you walk 5 metres, that's a scalar because it only tells you how far, not which way you went.

Vectors are more complex because they have both magnitude and direction. Displacement is a perfect example - walking 5 metres north is completely different from walking 5 metres south, even though the distance is the same.

When forces act on objects, you need to find the resultant force - the single force that has the same effect as all the individual forces combined. If forces push in the same direction, simply add them together. If they push in opposite directions, subtract the smaller from the larger.

For example, if you have 120N pushing right and 80N pushing left, your resultant force is 120N - 80N = 40N to the right. When forces act at angles to each other, you'll need Pythagoras' theorem $a² + b² = c²$ to find the resultant force magnitude.

Key Tip: Always draw force diagrams to scale - it makes visualising and calculating resultant forces much easier!