Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Grandfather clocks keep time using a pendulum of a fixed length.”
A simple pendulum's period depends only on length and g, not on mass or (small) amplitude.
T = 2π√(L/g)
Memory trick: Only length & g matter.
“Tune a radio and you're picking a frequency; its wavelength adjusts to keep the speed of light.”
For any wave, speed = frequency × wavelength.
v = fλ
Memory trick: v = fλ.
“Flick a rope for transverse; push a slinky for longitudinal.”
In transverse waves particles move perpendicular to travel (light, strings); in longitudinal waves they move along it (sound).
Memory trick: Sound = longitudinal; light = transverse.
“A singer can shatter a wine glass by matching its natural frequency.”
A system driven at its natural frequency oscillates with large amplitude.
Memory trick: Match natural frequency → big swing.
“Musicians tune instruments by listening for the beats to slow to zero.”
Two close frequencies together produce a throbbing whose beat frequency is their difference.
f = |f₁−f₂|
Memory trick: Beat freq = |f₁ − f₂|.
“An ambulance siren rises in pitch as it approaches and drops as it passes.”
Motion between source and observer shifts the observed frequency.
Memory trick: Approaching → higher pitch.
“Count the seconds between lightning and thunder — sound lags because it's far slower than light.”
Sound travels at about 343 m/s in air at room temperature, faster in warmer air.
Memory trick: ~340 m/s in air; faster when hot.
“A spark is very hot but tiny; a warm bath holds far more heat despite a lower temperature.”
Temperature measures average molecular kinetic energy; heat is energy transferred due to a temperature difference.
Memory trick: Heat flows; temperature is a state.
“Gaps are left between railway rails so they don't buckle on hot days.”
Most materials expand when heated as molecules vibrate more and spread apart.
Memory trick: Hotter → bigger.
“Coastal cities have mild weather because water heats and cools slowly.”
Heat needed to raise 1 kg of a substance by 1°C; water's is unusually high.
Q = mcΔT
Memory trick: High specific heat = slow to change temperature.
“Sweating cools you because evaporating water carries away latent heat.”
Heat absorbed or released during a change of state, at constant temperature.
Q = mL
Memory trick: Phase change hides the heat.
“A pan heats by conduction, boiling water circulates by convection, and the Sun reaches us by radiation.”
Heat moves by conduction (contact), convection (fluid currents) and radiation (electromagnetic waves).
Memory trick: Contact, currents, rays.
“You can't get more energy out of an engine than you put in — the universe keeps strict accounts.”
Energy conservation for gases: ΔU = Q − W, where W is work done by the gas.
ΔU = Q − W
Memory trick: Heat in = internal-energy rise + work out.
“Your coffee always cools to room temperature, never spontaneously reheats.”
Heat flows spontaneously from hot to cold, and no engine is perfectly efficient.
Memory trick: Disorder (entropy) tends to increase.
“A balloon shrinks in the cold and swells in the heat — PV = nRT in action.”
For an ideal gas, PV = nRT.
PV = nRT
Memory trick: Always use temperature in kelvin.
“It's gravity's electric cousin, but far stronger and able to push as well as pull.”
The force between two point charges is F = kq₁q₂/r² — like charges repel, unlike attract.
F = kq₁q₂/r²
Memory trick: Inverse-square, like gravity.
“The 'invisible reach' of a charge that pushes other charges around.”
Force per unit positive charge; field lines point away from + and toward − charges.
E = F/q
Memory trick: Field lines never cross.
“Voltage is 'electric height' — charges roll from high to low potential.”
Work done per unit charge to bring it from infinity to a point; a scalar.
V = kQ/r
Memory trick: Potential is a scalar; just add with sign.
“Camera flashes dump a capacitor's stored charge in a bright instant.”
A capacitor stores charge per volt; parallel-plate C = ε₀A/d.
C = ε₀A/d
Memory trick: Bigger plates, closer together → more storage.
“Defibrillators store energy in a capacitor and release it to restart a heart.”
A charged capacitor stores energy U = ½CV².
U = ½CV²
Memory trick: Energy grows with voltage squared.
“A car is a safe place in a lightning storm — the metal shell shields the inside.”
The electric field inside a conductor in equilibrium is zero — charges rearrange to cancel it.
Memory trick: Inside a conductor, E = 0.
“Every appliance you plug in obeys this simple pact between voltage, current and resistance.”
For many conductors, V = IR at constant temperature.
V = IR
Memory trick: V = IR.
“A long thin extension cord heats up more than a short thick one.”
Resistance R = ρL/A grows with length and falls with cross-sectional area.
R = ρL/A
Memory trick: Long & thin → more resistance.
“Home wiring is parallel so one bulb failing doesn't kill the rest.”
In series the current is shared and resistances add; in parallel the voltage is shared and 1/R values add.
Memory trick: Parallel total < smallest branch.