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Formula Sheets / Physics

Chapter 2

Mathematics in Physics

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Vectors Calculus in physics

Vectors

Resultant
$R = A^{2} + B^{2} + 2 A B cos θ,$ $tan α = \frac{B sin θ}{A + B cos θ}$
Dot and cross product
$A \cdot B = A B cos θ,$ $∣ A \times B ∣ = A B sin θ$
Components
$A_{x} = A cos θ, A_{y} = A sin θ,$ projection of $A$ on $B = \frac{A \cdot B}{B}$

Calculus in physics

$v = \frac{d x}{d t},$ $a = \frac{d v}{d t} = v \frac{d v}{d x},$ $x = \int v d t$
Small approximations
$(1 + x)^{n} \approx 1 + n x,$ $sin θ \approx tan θ \approx θ,$ $cos θ \approx 1 - \frac{θ ^{2}}{2} ($ small $)$
Maxima / minima
$\frac{d y}{d x} = 0;$ $\frac{d ^{2} y}{d x ^{2}} < 0$ max $, > 0$ min

Units and Dimensions Motion in One Dimension