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
“Judging a roof’s pitch by eye is like reading a graph’s slope from its visual tilt.”
The visual angle of a drawn line is not the numerical slope. Correctly compute m = Δy/Δx using the scales on the axes; forgetting the scale or using the angle gives an incorrect slope and intercept.
Memory trick: Use Δy/Δx, not visual tilt.
“A guitar string fixed at both ends shows a node at each end and the middle point moves up and down the most in the fundamental tone.”
In a standing wave formed by two identical waves traveling opposite directions, nodes are points of zero displacement and antinodes are points of maximum displacement. The distance between successive nodes is λ/2, and between a node and the nearest antinode is λ/4. A common error is treating node-to-antinode as λ/2, which gives wrong harmonic counts.
Memory trick: Node-to-node = λ/2, node-to-antinode = λ/4 – think ruler half-step vs quarter-step.
“Adding the brightness of many bulbs without their colors gives a wrong hue; similarly, adding only magnitudes of dB gives a wrong magnetic field.”
Biot-Savart contributions are vectors; you must sum them vectorially, respecting the perpendicular direction from Idℓ × r̂. Ignoring the cross-product direction (using only magnitudes) leads to incorrect net fields, especially for curved conductors.
Memory trick: Sum vectors, not just magnitudes.
“When you hear a speaker, the air particles move back-and-forth, never side-to-side, so no polariser can affect sound.”
A common misconception is that sound can be polarised. Sound waves are longitudinal; particle displacement is along the propagation direction, so there is no plane of vibration to select. Only transverse electromagnetic waves exhibit polarisation. Remember: polariser works on light, not sound.
Memory trick: Sound = longitudinal → no polarisation.
“A water pipe with a spring (inductor) resists rapid flow (high ω), while a rubber membrane (capacitor) blocks slow flow (low ω).”
For AC of angular frequency ω, capacitive reactance Xc = 1/(ωC) decreases with higher ω, whereas inductive reactance XL = ωL increases linearly with ω. Use these formulas whenever a sinusoidal source is present.
Xc = 1/(ωC), XL = ωL
Memory trick: C: 1/ω, L: ω → “C down, L up” with ω.
“An LED in a torch emits light when forward-biased, whereas a photodiode in a light sensor generates current when reverse-biased by incoming photons.”
An LED is forward-biased; electrons recombine with holes in the semiconductor lattice, releasing photons – electrical energy becomes light. A photodiode is reverse-biased; incident photons generate electron-hole pairs that are swept by the field, producing a current – light becomes electrical energy. Students often swap the bias directions.
Memory trick: LED forward = light out; Photodiode reverse = light in.
“Calibrating a kitchen scale before weighing flour removes the consistent 0.2 g bias, while shaking the scale each time creates random scatter.”
Systematic errors shift all readings by the same amount; they stem from mis-calibration or zero-offset and can be removed by correcting the instrument. Random errors cause measurements to vary around the true value due to unpredictable factors; averaging many trials reduces them. In exams, forgetting to identify which error you are addressing loses marks.
Memory trick: Fix bias → calibrate; scatter → average.
“A cricket ball slides sideways while falling straight down, showing separate x and y motions.”
In projectile motion the horizontal component has zero acceleration, so its velocity stays constant. The vertical component experiences only gravity, giving uniformly accelerated motion. Treat x and y independently; do not mix them.
Memory trick: x: const v; y: g-down
“When you push a heavy desk, the initial tug feels tougher than the steady slide that follows.”
Static friction acts up to its maximum μsN, adjusting to prevent motion; kinetic friction is constant μkN once sliding starts and is usually smaller. Remember that the static value is the limiting case, not a separate constant. In problems, use μs only when the body is at rest and about to move.
fₖ = μₖN
Memory trick: Static = Start, Kinetic = Keep going.
“A billiard ball that rebounds cleanly shows an elastic hit; a crumpled car after a crash shows an inelastic hit.”
Momentum of the whole system is always conserved because internal forces cancel. Only when the total kinetic energy before and after the impact are equal is the collision elastic; otherwise kinetic energy is lost to deformation, heat or sound, making it inelastic. In exam questions first verify KE conservation, not just the bounce direction.
Memory trick: Elastic = KE stays; Inelastic = KE ↓ (heat, sound)
“Opening a heavy gate, you push near the edge, not at the hinge, to feel the torque.”
Torque is the turning effect of a force: τ = r × F = rF sinθ. Only the component of force perpendicular to the radius produces torque. A common exam error is writing τ = rF without the sinθ or ignoring the lever-arm direction.
Memory trick: τ = rF sinθ → remember ‘rF sin’ like ‘rifle sin’
“When you drop a ball, Earth and the ball pull each other with a force that follows F = G m1 m2 / r².”
Any two masses attract each other with a force F = G·m₁m₂/r² directed along the line joining their centres. G is universal; the force is mutual. Exam trap: forgetting the vector direction or omitting one mass gives wrong magnitude.
Memory trick: G·m1·m2 over r² – G grabs both masses, r² pulls them apart.
“A scuba diver feels more pressure the deeper he goes, even though the tank’s width stays the same.”
Pressure at a depth h in a fluid is P = P0 + ρgh. It depends only on the fluid’s density, gravity and the vertical distance from the free surface, not on the container’s shape or the amount of liquid. In exams, students often forget to add atmospheric pressure or use the height of the liquid column instead of the depth measured from the surface.
Memory trick: P = P0 + ρgh – shape irrelevant.
“Twisting a screwdriver handle lets you feel shear strain; the resistance you feel is the material’s shear modulus.”
Young’s modulus (E) links normal stress to linear strain, bulk modulus (K) links hydrostatic pressure to volume strain, and shear modulus (G) links shear stress to angular strain. For isotropic linear elastic solids they are related: E = 2G(1+ν) and K = E/[3(1-2ν)], ν being Poisson’s ratio. A common trap is using the wrong modulus for a stress type or ignoring the ν-relations when given two of them.
Memory trick: E=2G(1+ν), K=E/[3(1-2ν)]
“Hear an ambulance siren: the pitch rises as it approaches and falls as it moves away.”
For sound speed v, f' = f (v+vo)/(v-vs). Add vo when the observer moves toward the source, subtract when receding. Subtract vs when the source moves toward the observer, add when it recedes. The exam trap is using the same sign for source and observer; the signs are opposite.
Memory trick: Toward: observer +, source – ; Away: observer –, source +.
“A steaming cup of tea cools down as heat moves into the cooler air around it.”
Heat always flows from a higher to a lower temperature without external work. This defines the direction of spontaneous processes and limits the efficiency of heat engines (η < 1). The trap: assuming a cyclic engine can convert all heat to work violates the second law.
Memory trick: Hot → Cold, No 100% engine (H C N)
“Like counting the number of water streams crossing a closed balloon – the total equals the charge inside divided by ε₀.”
Gauss’s law states that the net electric flux through any closed surface equals the enclosed charge divided by ε₀. It works because field lines start on positive charges and end on negatives, so counting them gives the net source. Trap: using an open surface or forgetting that flux is zero when no charge is inside.
Φ = q/ε₀
Memory trick: Φ = Q/ε₀ → ‘Φ’ sounds like ‘fee’, you pay fee for charge inside.
“In a copper wire, current is like a crowd in a hallway: the crowd moves fast, but each person walks only a few millimetres per second.”
Drift velocity v_d is the average speed of electrons under an electric field, given by v_d = I/(n A e). Because a metal contains ~10²⁸ carriers per m³, each electron moves only about 0.1 mm s⁻¹ for a 1 A current. Students often confuse this slow v_d with the rapid propagation of the electric signal, which travels near the speed of light.
Memory trick: v_d = I/(n A e) → ‘I over n A e’
“A long solenoid’s interior feels like the steady pull of a tightly wound spring when electricity flows through it.”
Inside a long solenoid the magnetic field is almost uniform and given by B = μ₀ n I, where n is turns per unit length. The contributions of each turn add parallelly, cancelling outside. The formula is valid only when the coil’s length is much greater than its diameter; a short coil gives a non-uniform field.
B = μ₀nI
Memory trick: B = μ₀·n·I – mu-zero, n, I in one line.
“The rainbow-like colors on a CD’s surface are bright and dark fringes created by the same interference that Young’s double-slit produces.”
Two coherent slits separated by d act as two point sources. On a screen at distance D (D≫d) bright fringes appear where the path difference d sinθ = mλ, giving fringe width β = λD/d. The derivation assumes small angles so sinθ≈tanθ≈θ. A frequent mistake is using D tanθ instead of D θ, which overestimates β.
β = λD/d
Memory trick: β = λ·(Screen-distance)/slit-sep → λD/d.
“Like a candle that loses half its wax in a fixed time, a radioactive sample loses half its atoms in its half-life.”
Half-life (T½) is the time for half the nuclei of a given isotope to decay; it is independent of the sample size. The mean life τ = T½/ln2 ≈ 1.44·T½. A common trap is using 0.693·T½ for τ – 0.693 is ln2, not its reciprocal.
Memory trick: τ ≈ 1.44 × T½ (since 1/ln2≈1.44).
“A microwave oven and a distant radio station both send waves that reach your antenna at exactly the same speed, like two runners on the same track obeying the same speed limit.”
In vacuum every electromagnetic wave, irrespective of its frequency, travels at c = 3×10⁸ m s⁻¹. For a plane wave the amplitudes obey E₀⁄B₀ = c. Frequency changes photon energy (E = hν) and wavelength, never the speed. The classic trap is to think higher-frequency rays travel faster.
Memory trick: c = E₀⁄B₀ for any EM wave in vacuum
“Riding a bike in rain, the drops seem to slant backward – that slant is v_rain minus your bike’s velocity.”
The velocity of A relative to B is v_A/B = v_A – v_B, a vector subtraction. Subtracting accounts for the observer’s motion, giving the true direction and speed seen. Exam trap: adding magnitudes or treating the subtraction as scalar leads to a wrong direction.
Memory trick: Relative = (object) – (observer) as vectors
“When ice melts in your drink, the temperature stays at 0 °C until all ice disappears.”
At a fixed pressure a substance does not change temperature while it melts or boils; the supplied heat is used to change phase, Q = mL. The kinetic energy of particles (temperature) rises only before or after the plateau, described by Q = mcΔT. In exams, never apply mcΔT across the flat part of a T-Q graph.
Memory trick: Flat = Latent, slope = sensible.