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
“Balancing a ruler on a fingertip shows its centre of mass is at the midpoint.”
The centre of mass (COM) is the point where the total mass of a body can be considered to act, giving the same external effect as the distributed mass. For uniform bodies, COM coincides with the geometric centre. Trap: assuming COM always lies inside; for L-shaped objects it can be outside the material.
Memory trick: COM = balance point of mass
“A planet at twice Earth’s orbital radius takes about 2.8 times longer to circle the Sun.”
Kepler’s third law for bodies around the same central mass: T² = (4π²/GM) r³, so T² ∝ r³. The constant 4π²/GM is identical for all planets of the Sun. A common mistake is to compare T² and r³ of objects orbiting different masses without adjusting the constant.
T² ∝ r³
Memory trick: T²∝r³ → (T²)¹ᐟ³ gives r.
“A water droplet beads on a waxed car hood because surface molecules pull tightly together.”
Surface tension is the energy per unit area caused by cohesive forces pulling surface molecules inward, acting like a stretched elastic sheet. Measured in N/m. Trap: it acts along the surface, not throughout the bulk; use γ·L for force on a line.
Memory trick: Surface tension = surface's tight rope
“A metal spring returns to its original length after a gentle push, but if you press it too hard it stays compressed.”
The proportional limit marks the end of the straight-line σ-ε graph; stress is still proportional to strain only up to this point. The elastic limit is the maximum stress at which the material fully recovers after load removal; it can lie beyond the proportional limit. Trap: assuming elastic limit equals fracture or that linearity holds up to elastic limit.
Memory trick: Proportional = straight line; Elastic = full recovery.
“Pushing a playground swing at its natural rhythm makes it soar higher with each push.”
Resonance occurs when an external periodic force matches a system’s natural frequency, causing amplitude to grow markedly. Energy builds because each push adds in phase. Trap: assuming any large amplitude means resonance; need matching frequency, not just strong force.
Memory trick: Resonance = ‘R’ for ‘Right timing’
“Your hand feels warmth from a fireplace (radiation), the rising hot air (convection), and the metal pot you touch (conduction).”
Heat transfer occurs by conduction (direct molecular collisions in solids), convection (bulk motion of fluids), and radiation (electromagnetic waves). Each mode dominates in different situations; neglecting one can cause loss of marks.
Memory trick: Conduction = touch, Convection = flow, Radiation = rays.
“Charging a flashbulb stores energy U = ½CV², which later releases as a bright flash.”
Energy in a capacitor is U = ½CV², obtained by integrating dU = V dQ. Because of the V² term, a small rise in voltage gives a large increase in stored energy. Mistake to avoid: using U = CV² without the ½ factor.
U = ½CV²
Memory trick: U = ½ C V², half the CV².
“A 60 W LED bulb glows because the 120 V supply and the 0.5 A it draws satisfy P = VI.”
Electric power is the rate of electrical energy conversion: P = VI. Substituting V = IR gives P = I²R, and I = V/R gives P = V²/R, but the latter forms assume resistance stays constant (ohmic). In exams avoid using V²/R for a filament lamp whose resistance changes with temperature.
P = VI
Memory trick: P = V·I; V=IR → I²R, I=V/R → V²/R (only if R constant)
“A bicycle dynamo lights a headlamp as the wheel spins, turning coil flux into alternating voltage.”
Rotating a coil of N turns in a uniform B gives emf ε = NABω sin(ωt). The emf peaks when the coil’s plane is parallel to B (its normal ⟂ B), i.e., when the flux changes fastest. The usual trap is confusing this with the position of maximum flux, where emf is zero.
Memory trick: Max ε when coil plane ∥ B (normal ⟂ B).
“Reading glasses for farsightedness are convex lenses that bring distant objects to a nearer focus.”
A convex (converging) lens has positive focal length and brings parallel rays to a real focus on the opposite side; used for correcting hyperopia. A concave (diverging) lens has negative focal length, spreads rays as if they originated from a virtual focus; used for myopia. The trap: sign of f decides image nature; mixing them flips answer.
Memory trick: Convex = +f, converges; Concave = –f, diverges.
“A gram of matter annihilated with antimatter would release enough energy to power a city for a day.”
Mass and energy interconvert via E = mc²; because c² ≈ 9×10¹⁶ J kg⁻¹, even 1 g yields ~9×10¹³ J. Trap: using grams without converting to kilograms or mixing MeV units.
E = mc²
Memory trick: c² ≈ 9×10¹⁶ J/kg; tiny mass → huge J.
“Polarized sunglasses block the electric component that oscillates in a particular direction, showing E is perpendicular to travel.”
In a plane EM wave, E, B and the propagation vector k are mutually orthogonal; E×B points along k and gives the Poynting vector. Because the fields are transverse, they have no component along the travel direction. Trap: drawing E or B parallel to k—always keep them at right angles.
Memory trick: E ⟂ B ⟂ k
“A water fountain’s arc sketches the same parabola as the ideal projectile path.”
Eliminate t from x = u cosθ t and y = u sinθ t – ½gt² to get y = x tanθ – (g x²)/(2u² cos²θ), a parabola. The term cos²θ in the denominator determines the curvature. Dropping it makes the curve too steep, a typical mistake.
Memory trick: tanθ gives slope; cos²θ in denominator shapes curve.
“If you blend 1 L of water at 80 °C with 3 L at 20 °C, the final temperature is not 50 °C but closer to 20 °C.”
Final temperature after mixing is weighted by heat capacities: Tf = (Σ mi ci Ti)/(Σ mi ci). The body with larger m c pulls the equilibrium toward its initial temperature. Using a simple arithmetic mean ignores this weighting.
Memory trick: Weighted avg, not simple avg: Σ m c T / Σ m c
“RMS speed is like RMS voltage: square each speed, average them, then take the square root.”
Root-mean-square speed v_rms = √(⟨v²⟩) = √(3k_B T/m). It is the square root of the mean of the squares of speeds, not the arithmetic mean speed. Trap: confusing v_rms with average speed, leading to wrong pressure calculations.
Memory trick: RMS = √(mean of v²), never mean v
“Moving a charge along a flat floor (equipotential) needs no effort despite a strong wind (field) blowing perpendicular.”
On an equipotential surface the potential is constant, so moving a charge anywhere on it requires zero work. Electric-field lines intersect equipotentials at right angles. Zero work does NOT mean the field is zero; it only has no component along the surface.
Memory trick: Work zero → E ⟂ surface
“When you use a smartphone compass, the dip angle tells how much the needle tilts below the horizon, not how far it points up.”
Earth’s magnetic field at any location is described by declination (horizontal angle from geographic north), dip or inclination (angle the field makes with the horizontal plane), and the horizontal component strength. Dip is measured from the horizontal, not from the vertical. Mixing them gives wrong component values in vector problems.
Memory trick: Dip = tilt from horizontal; declination = map turn.
“A ball deep in a well has negative potential; the rim (infinity) is set to zero.”
Hydrogen’s bound-state energies are negative because zero is defined for a free electron at infinity. The ground state (n=1) has the most negative energy (most tightly bound); as n increases the energy rises toward zero, and at n→∞ the electron is ionised. Remember the sign convention.
Memory trick: Deeper well = more negative.
“Comparing total binding energies is like judging a marathon by total distance; you need the average per runner – binding energy per nucleon.”
Stability is measured by B/A. The curve peaks at A≈56 (Fe/Ni) with ~8.8 MeV per nucleon. Light nuclei release energy by fusion, heavy by fission. Trap: using total B alone misleads across different A.
Memory trick: Peak B/A at A≈56 → iron
“Finding the slope of a distance-time graph is like measuring the steepness of a hill on a map.”
A straight-line graph follows y = mx + c. The slope m = Δy/Δx must be taken from two well-separated points on the best-fit line, and its units are those of y divided by those of x. Using any two raw points or ignoring axis scales yields a wrong slope.
Memory trick: Slope = rise/run on graph, keep units.
“A guitar string fixed at both ends vibrates with nodes at the ends and a belly in the middle.”
Opposite-travelling identical waves create nodes (zero displacement) and antinodes (maximum). Node-to-node distance = λ/2, node-to-adjacent antinode = λ/4. No net energy transport along the string; forgetting λ/4 spacing loses points.
Memory trick: Node-node λ/2, node-antinode λ/4.
“Swirling a spoon in coffee creates tiny whirls that add up to the overall vortex, just as each current element dℓ×r̂ adds to the magnetic field.”
Biot-Savart law: dB = (μ₀/4π)·(I dℓ × r̂)/r². The direction follows the right-hand rule (thumb along Idℓ, fingers toward point). Integrate these vector contributions over the conductor. Trap: treating dB as a scalar magnitude and ignoring its direction.
Memory trick: dℓ × r̂ gives direction; keep vector.
“Sunglasses block glare by allowing only the vertical component of sunlight to pass, illustrating light’s transverse nature.”
Light, being a transverse wave, oscillates perpendicular to its travel direction, so its electric field can be confined to a single plane—polarisation. Longitudinal waves like sound lack such perpendicular oscillations and cannot be polarised. Exam trap: assuming any wave can be polarised.
Memory trick: Only transverse waves (e.g., light) polarise.
“When you tune a radio to a station, the L and C cancel at resonance, making the circuit’s impedance drop to just R.”
At resonance in a series LCR circuit (f = 1/2π√LC), inductive reactance XL equals capacitive reactance Xc, so they cancel and the total impedance Z = R, its minimum. The current is maximal, not the impedance. The trap: assuming resonance gives maximum impedance.
Memory trick: Resonance: XL = Xc → Z = R (minimum).