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.
300 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.
“Telling someone you walked 5 km is a scalar; telling them 5 km north is a vector — direction changes everything.”
A scalar has only magnitude (mass, time, speed); a vector has magnitude AND direction (displacement, velocity, force).
Memory trick: If direction matters, it's a vector.
“Checking dimensions is the physicist's spell-check for equations.”
Force has dimensions [M L T^-2], from mass times acceleration.
[M L T^-2]
Memory trick: Force = mass × accel → M × (L/T²).
“Hold a finger up and blink each eye: it jumps. Astronomers use Earth's orbit as their 'two eyes'.”
Very large distances (like to nearby stars) are found by parallax — the apparent shift of an object against a far background when viewed from two points.
Memory trick: Bigger baseline → measure farther.
“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.
“Cruise control aims for uniform motion; city traffic is relentlessly non-uniform.”
Uniform motion covers equal distances in equal times (zero acceleration); non-uniform motion does not.
Memory trick: Constant velocity = uniform.
“It's the promise that steady acceleration adds speed at a fixed rate every second.”
For constant acceleration, final velocity v = u + at.
v = u + at
Memory trick: 'velocity = start + accel×time'.
“The ½at² term is why a dropped ball falls farther in each successive second.”
Displacement under constant acceleration is s = ut + ½at².
s = ut + ½at²
Memory trick: distance = start×time + half×accel×time².
“When the clock isn't given, this is your go-to equation.”
v² = u² + 2as links velocity and displacement without time.
v² = u² + 2as
Memory trick: No 't'? Use v² = u² + 2as.
“Apollo 15 dropped a hammer and a feather on the airless Moon — they hit the ground together.”
Near Earth every object falls with the same acceleration g ≈ 9.8 m/s², independent of mass (ignoring air).
g ≈ 9.8 m/s²
Memory trick: No air → mass doesn't matter.
“A bullet fired horizontally and one dropped from the same height hit the ground at the same instant.”
In projectile motion the horizontal motion (constant velocity) and vertical motion (free fall) are completely independent.
Memory trick: Split every projectile into x and y.
“Long-jumpers and shot-putters instinctively launch near 45° for maximum distance.”
For a projectile on level ground, range is maximum at a launch angle of 45°.
R = u²sin2θ/g
Memory trick: 45° = farthest throw.
“Two trains passing feel terrifyingly fast; two trains side-by-side at the same speed feel still.”
The velocity of A relative to B is the vector v(A) − v(B).
v(AB) = v(A) − v(B)
Memory trick: Same direction subtract, opposite add.
“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.
“The same push gives a shopping trolley a big shove but barely moves a truck.”
The net force equals the rate of change of momentum, and for constant mass F = ma.
F = ma
Memory trick: Force = mass × acceleration.
“A rocket flies by throwing gas down; the gas pushes the rocket up.”
Every action has an equal and opposite reaction, acting on two different bodies.
Memory trick: Action & reaction: different bodies, never cancel.
“A slow-moving truck can carry more momentum than a fast bullet.”
Momentum p = mv is 'mass in motion'; a net force is needed to change it.
p = mv
Memory trick: p = mv.
“A gun recoils backward exactly to balance the forward momentum of the bullet.”
With no external force, total momentum of a system stays constant.
Memory trick: No external force → total p is fixed.
“Airbags save lives by stretching the stopping time, so the same momentum change needs far less force.”
Impulse = force × time = change in momentum.
J = F·t = Δp
Memory trick: More time → less force for the same stop.
“It's harder to get a heavy box moving than to keep it sliding — static beats kinetic.”
Static friction (up to μₛN) prevents motion and self-adjusts; kinetic friction (μₖN) opposes sliding and is usually smaller.
fₖ = μₖN
Memory trick: Starting is harder than keeping going.
“Whirl a stone on a string — the string's inward pull is what stops it flying off.”
Circular motion needs a net inward (centripetal) force of mv²/r.
F = mv²/r
Memory trick: It always points to the centre.
“Race tracks tilt inward on curves so cars can corner fast without skidding.”
Roads are banked so a component of the normal force supplies the centripetal force, reducing reliance on friction.
tanθ = v²/rg
Memory trick: Tilt supplies the turn.
“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.
“Doubling your car's speed quadruples its crash energy — why speed limits matter so much.”
Energy of motion, KE = ½mv² — it grows with the square of speed.
KE = ½mv²
Memory trick: Speed doubles → KE quadruples.