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
“Every measurement you'll ever make traces back to just seven agreed-upon units.”
The seven SI base units are metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity).
Memory trick: 'Metre Kid Sat A King Made Candles' → m, kg, s, A, K, mol, cd.
“Run one full lap of a track and your distance is 400 m but your displacement is zero — you're back where you started.”
Distance is total path length (scalar, never decreases); displacement is the straight-line vector from start to finish.
Memory trick: Round trip: distance big, displacement zero.
“When a bus brakes suddenly you lurch forward — your body wanted to keep moving.”
A body stays at rest or in uniform motion unless acted on by a net external force.
Memory trick: No net force → no change in motion.
“Carrying a bag across a level floor does no work against gravity — the lift force is vertical, the motion horizontal.”
Work = force × displacement in the force's direction, W = Fd·cosθ; a perpendicular force does zero work.
W = Fd cosθ
Memory trick: Perpendicular force → zero work.
“You push a door at its handle, not near the hinge — more distance, more turn.”
Torque τ = force × perpendicular distance is the turning effect of a force.
τ = rF sinθ
Memory trick: Torque = force × lever arm.
“The same law that drops an apple holds galaxies together.”
Every two masses attract with F = Gm₁m₂/r².
F = Gm₁m₂/r²
Memory trick: Inverse-square: double distance, quarter force.
“Your ears hurt at the bottom of a swimming pool because water pressure grows with depth.”
Pressure increases with depth: P = P₀ + ρgh.
P = P₀ + ρgh
Memory trick: Deeper = higher pressure.
“Stretch a spring gently and it springs back; pull too far and it stays bent.”
Within the elastic limit, stress is proportional to strain.
stress ∝ strain
Memory trick: Small stretch → restoring force ∝ stretch.
“A child on a swing, a guitar string, a vibrating atom — all sing the SHM song.”
Oscillation where the restoring force is proportional to and opposite the displacement (F = −kx).
F = −kx
Memory trick: Force pulls back ∝ how far you pushed.
“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.
“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.
“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.
“This sideways push bends particle beams in old TV tubes and particle accelerators.”
A magnetic field exerts F = qvB sinθ on a moving charge, always perpendicular to its velocity.
F = qvB sinθ
Memory trick: Magnetic force does no work.
“It's why a mirror gives you a clean, predictable image.”
The angle of incidence equals the angle of reflection, and both lie in one plane.
Memory trick: Angle in = angle out.
“Einstein won his Nobel for explaining this — proof that light comes in packets.”
Light ejects electrons from a metal only above a threshold frequency, regardless of intensity.
Memory trick: Frequency decides IF; intensity decides HOW MANY.
“Light, radio and X-rays are the same wave at different frequencies.”
Oscillating electric and magnetic fields travelling at the speed of light, needing no medium.
c = 3×10⁸ m/s
Memory trick: No medium needed.
A vector is one arrow, but we may replace it by perpendicular x- and y-parts that together produce exactly the same effect. If the vector A makes angle theta with +x, then A_x = A cos(theta) and A_y = A sin(theta); signs come from the actual directions, not from the formula.
Memory trick: draw the arrow first; cosine sits beside the marked angle, sine sits opposite it, then assign signs.
Temperature tells how hot a body is and sets the direction of heat flow; heat is energy transferred because of a temperature difference. A bucket of warm water can contain more thermal energy than a cup of hotter water.
Memory trick: temperature decides direction; heat is energy in transit.
Gas pressure comes from molecular collisions with container walls. Each collision changes molecular momentum; the wall experiences the equal and opposite momentum transfer spread over time and area.
Memory trick: more frequent or harder wall hits mean higher pressure.
Electric potential at a point is potential energy per unit test charge. Because it is a scalar, contributions from many source charges add algebraically with their signs.
Memory trick: fields need directions; potentials need signs.
A bar magnet behaves like a magnetic dipole. Its moment points from south to north inside the magnet and determines the torque m x B in an external field.
Memory trick: dipole moment points S to N through the magnet.
Most alpha particles pass through foil because atoms are mostly empty space; rare large deflections show that positive charge and most mass occupy a tiny nucleus.
Memory trick: Rutherford found the nucleus; Bohr addressed stable energies.
Nuclear radius scales as R = R_0 A^(1/3), so volume scales with nucleon number A. Because mass also scales with A, nuclear density is approximately constant across nuclei.
Memory trick: mass number grows with volume, so radius grows by the cube root.
An instrument cannot honestly resolve changes smaller than its least count. A final reading combines the main-scale reading, coinciding-division contribution, and the zero-error correction with correct sign.
Memory trick: correct reading = observed reading - zero error.