Scalars vs. Vectors
Overview
Scalars have magnitude only: distance, speed, time, mass, temperature. Vectors have both magnitude and direction: displacement, velocity, acceleration, force. When solving problems, always check whether a quantity is a scalar or vector — this determines whether you can simply add values or must account for direction.
Scalars — magnitude only
A scalar is fully described by a number and a unit. You can add, subtract, and compare scalars using ordinary arithmetic. In physics, common scalars include: distance (how far an object travels along its path), speed (the rate of covering distance), time, mass, energy, temperature, and pressure. If you walk 3 km around a park, the distance is 3 km — no direction needed.
Vectors — magnitude AND direction
A vector requires both a magnitude and a direction to be meaningful. Displacement is the straight-line distance from start to finish with a specified direction. Velocity is speed in a given direction. Force, acceleration, and momentum are also vectors. In IB Physics, vectors are often written in bold (F) or with an arrow (→F). You cannot simply add vector magnitudes — direction must be accounted for.
Resolving vectors into components
Any vector F at angle θ to the horizontal can be split into two perpendicular components: the horizontal component Fx = F cos θ and the vertical component Fy = F sin θ. To add multiple vectors, resolve each into x and y components, sum all x-components and all y-components separately, then reconstruct the resultant: R = √(Rx² + Ry²) at angle φ = arctan(Ry/Rx).
- ⚠Adding vector magnitudes directly without considering direction (e.g. two 5 N forces don't always give 10 N)
- ⚠Forgetting to state direction for a vector quantity in exam answers
- ⚠Confusing distance (scalar, total path) with displacement (vector, straight-line start to end)
- ⚠Swapping sin and cos — remember: cos θ gives the component adjacent (horizontal) to the angle, sin θ gives opposite (vertical)
Active Recall Check
Close the lesson and answer 3 quick questions from memory. This is the most effective way to lock in what you just read.