Vectors and scalars · Grade 8
A scalar has only a size (like 20 m/s or 5 kg). A vector has a size and a direction (like 20 m/s north). Forces, velocities and displacements are vectors, so we add them by drawing arrows or by using Pythagoras and trigonometry.
Key facts
- Scalars: distance, speed, mass, time, energy, temperature, power.
- Vectors: displacement, velocity, acceleration, force, weight, momentum.
- Vectors in the same line add or subtract; vectors at right angles combine with Pythagoras.
- Direction of a resultant: use tan θ = opposite ÷ adjacent (or a bearing from north).
- Resolving: a vector F at angle θ to the horizontal has components F cos θ (horizontal) and F sin θ (vertical).
- On a slope at angle θ, weight splits into mg sin θ down the slope and mg cos θ into the slope.