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Grade 12 Physical Sciences: Key Formulas

Core physics and chemistry formulas for South African NSC Physical Sciences: mechanics, electricity, waves, quantitative chemistry and equilibrium.

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Newton's second law

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Newton's second law

F_{n e t} = ma

Weight

w = m g

, with

g = 9, 8

m·s⁻² near the Earth's surface.

Momentum

p = m v

(a vector quantity, unit kg·m·s⁻¹).

Impulse and change in momentum

F_{n e t} Δ t = Δ p = m v_{f} - m v_{i}

Kinetic energy

E_{k} = \frac{1}{2} m v^{2}

Gravitational potential energy

E_{p} = m g h

Work done by a constant force

W = F Δ x cos θ

Work-energy theorem

W_{n e t} = Δ E_{k} = E_{k f} - E_{k i}

Equation of motion: velocity

v_{f} = v_{i} + a Δ t

Equation of motion: displacement

Δ x = v_{i} Δ t + \frac{1}{2} a Δ t^{2}

Equation of motion: velocity and displacement

v_{f}^{2} = v_{i}^{2} + 2 a Δ x

Coulomb's law

F = \frac{k Q _{1} Q _{2}}{r ^{2}}

, with

k = 9 \times 1 0^{9}

N·m²·C⁻².

Electric field strength

E = \frac{F}{q} = \frac{k Q}{r ^{2}}

Ohm's law

R = \frac{V}{I}

Electrical power

P = V I = I^{2} R = \frac{V ^{2}}{R}

Resistors in series

R_{s} = R_{1} + R_{2} + R_{3} + \dots

Resistors in parallel

\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

Emf of a battery with internal resistance

ε = I (R + r)

Faraday's law of induction

ε = - N \frac{ΔΦ}{Δ t}

Wave speed

v = f λ

Energy of a photon

E = h f = \frac{h c}{λ}

, with

h = 6, 63 \times 1 0^{- 34}

J·s.

Photoelectric equation

E = W_{0} + E_{k (ma x)}

, i.e.

h f = h f_{0} + \frac{1}{2} m v_{ma x}^{2}

Doppler effect (sound)

f_{L} = \frac{v \pm v _{L}}{v \pm v _{s}} f_{s}

Amount of substance from mass

n = \frac{m}{M}

Concentration of a solution

c = \frac{n}{V}

(mol·dm⁻³).

Gas volume at STP

n = \frac{V}{22 , 4}

, with V in dm³.

p H = - lo g [H_{3} O^{+}]

; at 25 °C,

p H + pO H = 14

Equilibrium constant for

a A + b B ⇌ c C + d D

K_{c} = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}

Standard cell potential

E_{ce l l}^{θ} = E_{c a t h o d e}^{θ} - E_{an o d e}^{θ}

General formula of the alkanes, alkenes and alkynes

Alkanes

C_{n} H_{2 n + 2}

; alkenes

C_{n} H_{2 n}

; alkynes

C_{n} H_{2 n - 2}

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