IB Physics Annotated Formulas

Each equation paired with a brief idea, so you remember what it means — not just how it looks.

Mechanics • Thermal • Waves • Fields • Nuclear & Quantum

Topic-wise Annotated Map

Read the note first, then the equation. Let the concept lead, and the formula will follow.

$v = u + at$
Final velocity for constant acceleration.
$s = ut + \tfrac{1}{2}at^{2}$
Displacement with constant acceleration.
$v^{2} = u^{2} + 2as$
Links velocities, acceleration, and displacement (no time).
$v_{\text{avg}} = \dfrac{\Delta s}{\Delta t}$
Average velocity = total displacement ÷ time.
$a = \dfrac{\Delta v}{\Delta t}$
Definition of acceleration.
$F = ma$
Newton’s second law (resultant force).
$W = F s \cos\theta$
Work done by a constant force along displacement.
$p = mv$
Linear momentum of a particle.
$F\Delta t = \Delta p$
Impulse = change in momentum.
$P = \dfrac{\Delta W}{\Delta t} = Fv$
Power = rate of work; for constant speed: P = Fv.
$E_{k} = \tfrac{1}{2}mv^{2}$
Kinetic energy of a moving mass.
$E_{p} = mgh$
Gravitational potential energy near Earth’s surface.

$a_{c} = \dfrac{v^{2}}{r} = \omega^{2} r$
Centripetal acceleration towards the centre.
$F_{c} = \dfrac{mv^{2}}{r} = m \omega^{2} r$
Centripetal force needed for circular motion.
$F = G \dfrac{m_{1}m_{2}}{r^{2}}$
Newton’s law of universal gravitation.
$g = G \dfrac{M}{r^{2}}$
Gravitational field strength of a mass M.
$\dfrac{GMm}{r^{2}} = \dfrac{mv^{2}}{r}$
Orbital condition: gravity provides centripetal force.

$Q = mc\Delta T$
Heat added to change temperature (no phase change).
$Q = mL$
Heat for phase change at constant temperature.
$pV = nRT$
Ideal gas equation of state.
$\langle E_{k} \rangle = \tfrac{3}{2} k_{B} T$
Mean kinetic energy of particles in an ideal gas.
$U = \tfrac{3}{2} nRT$
Internal energy of a monatomic ideal gas.

$I = \dfrac{Q}{t}$
Electric current = charge per unit time.
$V = \dfrac{W}{q}$
Potential difference = work done per unit charge.
$V = IR$
Ohm’s law for a resistor.
$P = VI = I^{2}R = \dfrac{V^{2}}{R}$
Electrical power in different forms.
$R_{\text{series}} = R_{1} + R_{2} + \dots$
Total resistance in series.
$\dfrac{1}{R_{\text{parallel}}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} + \dots$
Total resistance in parallel.
$R = \rho \dfrac{L}{A}$
Resistance of a wire: depends on length and area.

$v = f\lambda$
Wave speed relation (frequency × wavelength).
$T = \dfrac{1}{f}$
Period = 1 ÷ frequency.
$I = \dfrac{P}{A}$
Intensity = power per unit area.
$n = \dfrac{c}{v}$
Refractive index from speed in medium.
$n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}$
Snell’s law of refraction.
$a = -\omega^{2} x$
SHM acceleration: proportional to displacement, opposite direction.
$x = x_{0}\cos(\omega t)$
Displacement in SHM as a function of time.
$\omega = 2\pi f = \dfrac{2\pi}{T}$
Angular frequency and its links to f and T.

$E = k \dfrac{Q}{r^{2}}$
Electric field of a point charge (magnitude).
$F = qE$
Force on a charge in an electric field.
$V = k \dfrac{Q}{r}$
Electric potential of a point charge.
$C = \dfrac{Q}{V}$
Capacitance definition.
$F = qvB\sin\theta$
Magnetic force on a moving charge.
$F = BIL\sin\theta$
Magnetic force on a current-carrying wire.
$\Phi = BA\cos\theta$
Magnetic flux through a loop of area A.
$\mathcal{E} = \dfrac{\Delta \Phi}{\Delta t}$
Induced emf from changing flux (Faraday’s law).

An equation is just a compressed sentence. Expand it in your mind every time you use it.

Ask: what does each symbol represent, and in which situations does this relationship hold?

This is how formulas become tools for thinking, not items to memorise.