Vectors & forces
Start with the model and its assumptions. These relationships use SI units unless you convert every quantity consistently.
Vectors & forces
| Relationship | Formula | When it applies |
|---|---|---|
| Components | Aₓ = A cos θ; Aᵧ = A sin θ | θ is measured counterclockwise from +x. |
| Magnitude & direction | |A| = √(Aₓ² + Aᵧ²); θ = atan2(Aᵧ, Aₓ) | Direction is undefined when |A| = 0. |
| Unit vector | Â = A / |A| | Dimensionless; requires A ≠ 0. |
| Vector products | A · B = |A||B| cos θ; |A × B| = |A||B| sin θ | Dot product is scalar; cross product follows the right-hand rule. |
| Newton’s second law | ΣF = ma | In an inertial frame, for constant mass. |
| Weight & friction | W = mg; fₛ ≤ μₛN; fₖ = μₖN | Static friction adjusts to prevent relative slipping, up to its maximum. |
| Spring force | Fₓ = −kx | x is displacement from the relaxed position; linear elastic regime. |
Find definitions and the original reference tables in the glossary →