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
“Adding hill heights gives a number, not an arrow; potentials work the same way.”
A frequent mistake is to add potentials as vectors or to drop the sign of a negative source charge. Since V is a scalar, you must sum the individual potentials with their proper signs. Ignoring the sign gives an incorrect total potential.
Memory trick: Potential = scalar, keep sign
“A student watching iron filings think field lines go north-to-south, so they flip the dipole direction, but the magnet’s moment still runs south-to-north inside.”
Magnetic moment direction is defined from south to north inside the magnet, while external field lines run from north to south. The torque formula uses m × B, so reversing m gives opposite torque. Exams often penalise the sign error when students draw the moment along the field lines.
Memory trick: Field N→S, moment S→N.
“Rutherford gave the shape of a bowl; Bohr added the steps that let a marble stay without rolling.”
Rutherford’s scattering experiment proved a compact, massive nucleus but did not explain why atoms are stable or why they emit line spectra. Those questions were answered later by Bohr’s quantised orbits. Beware of attributing spectral lines to Rutherford’s model.
Memory trick: Rutherford → nucleus, Bohr → spectra.
“A watermelon and a grape feel equally firm; nuclei, from hydrogen to uranium, keep the same “mass per volume”.”
Nuclear radius follows R = R0·A^(1/3) (R0≈1.2 fm). Hence volume ∝ A and mass ∝ A, giving almost constant density ≈2.3×10¹⁷ kg m⁻³ for all nuclei. The common trap is assuming radius ∝ A; the cube-root dependence must be used in size problems.
Memory trick: R ∝ cube-root of A → think “cube side = nucleons”.
“When you set a kitchen scale to zero, adding the displayed offset is like adding extra tip to a bill.”
A positive zero error must be subtracted from the observed reading; a negative zero error is added. Many students add the error regardless of its sign, which flips the result.
Memory trick: Zero error + → subtract; zero error – → add.
“A ship’s sonar ping keeps its pitch when it moves from water to air, yet its wavelength shortens because the speed of sound drops in air.”
Across a boundary the source frequency remains unchanged. Wave speed changes with the medium, so λ = v/f adjusts accordingly. In water v≈1500 m/s giving a long λ; in air v≈340 m/s the λ becomes much shorter. The exam often flips the direction—remember λ follows v, not the other way.
Memory trick: Higher v → longer λ (f fixed)
“A cyclist riding straight under a uniform magnetic field feels no sideways push, just as a charge moving parallel to B feels no force.”
The magnetic force magnitude is F = qvB sinθ, where θ is the angle between v and B. A common error is to write F = qvB without the sinθ factor, which would give a force even when v is parallel to B. The correct rule: only the component of v perpendicular to B contributes; if v ∥ B, F = 0.
Memory trick: F = qvB sinθ → sin0=0, so no force when v∥B
“Two ordinary bulbs placed side by side never give clear Young’s fringes, unlike a single lamp split by a slit.”
A frequent error is assuming any two lamps can interfere. Coherence requires a fixed phase relation, which ordinary independent bulbs lack. Hence no steady fringes appear; only a single source split into two coherent beams does.
Memory trick: Independent bulbs ≠ coherent; split one source = coherent.
“Increasing the frequency on a signal generator makes a capacitor’s reactance drop, so more AC current passes through the circuit.”
Reactance is not a fixed resistance; it varies with the source frequency. For a capacitor Xc=1/ωC (decreases as ω rises) and for an inductor XL=ωL (increases as ω rises). A common trap is using Xc or XL as a constant R when the frequency changes, leading to wrong impedance or power calculations.
Memory trick: Xc↓ with f, XL↑ with f – ‘C down, L up’.
“When you plug a diode backward into a circuit board, the LED never lights – it won’t conduct like a resistor.”
A diode does not conduct equally both ways. Forward bias lowers the junction barrier, allowing large current; reverse bias raises the barrier, permitting only a negligible leakage current. The common mistake is to draw a symmetric I-V curve – remember the reverse branch is almost flat.
Memory trick: Diode ≠ two-way pipe; only forward opens.
“Pushing a shopping cart, the force you feel equals its mass times the acceleration you give it, giving dimensions M L T⁻².”
Force is defined by Newton’s second law, F = m·a, so its dimensional formula is [M][L][T]⁻². This follows because mass carries M and acceleration carries L T⁻². Beware mixing up with pressure, whose dimensions are [M][L]⁻¹[T]⁻².
[M L T⁻²]
Memory trick: F = m·a → M·L/T²
“A ball thrown upward slows by 9.8 m/s each second, so after 3 s its speed is initial minus 29.4 m/s.”
For constant acceleration, the final velocity equals the initial velocity plus the product of acceleration and elapsed time. It follows from a = Δv/Δt. Keep the signs of a and u consistent; a wrong sign flips the result.
v = u + at
Memory trick: U + AT = V
“When you jump, the floor pushes you up with a force equal to your push down.”
Every action on one body has an equal and opposite reaction on another body; the two forces act on different objects, so they never cancel in a single free-body diagram. In problems, draw each force on the body it acts upon.
Memory trick: Action-reaction act on different bodies.
“When a roller coaster descends a hill, the drop’s work equals the increase in its kinetic energy.”
The net work done by all forces on a body equals the change in its kinetic energy: Wnet = ΔKE. Individual forces may do positive or negative work, but only the sum matters. Trap: mixing individual work with net work.
W = ΔKE
Memory trick: Wnet = ΔKE, sum of works = Δ(½mv²)
“A spinning ice skater pulls arms in and spins faster, showing L = Iω stays constant.”
When net external torque is zero, the product I ω (angular momentum) remains unchanged. If I decreases, ω must increase proportionally. A trap: assuming linear speed is conserved; only angular momentum, not kinetic energy, is guaranteed.
L = Iω
Memory trick: No torque → L constant → I↓ ⇒ ω↑
“A rocket needs about 11.2 km/s to leave Earth, just enough to outrun the pull described by v = √(2GM/R).”
Escape velocity vₑ = √(2GM/R) is the minimum speed to reach infinity with zero residual speed; it depends only on the planet’s mass and radius. Trap: confusing escape speed with orbital speed – escape is √2 times the circular orbital speed at the same radius.
v = √(2GM/R)
Memory trick: Escape = √2 × orbital speed – remember the ‘escape factor’
“A steel ship floats because water pushes up with a force equal to the weight of water it displaces.”
Buoyant force = weight of the displaced fluid = ρ_fluid · V_displaced · g, acting upward. It depends on displaced volume, not on the object's material unless fully submerged. Exam often mixes up volume of object vs displaced volume.
Memory trick: Buoyancy = weight of water moved
“When you press a finger on a balloon, the pressure you apply is stress, while the balloon’s tiny expansion relative to its size is strain.”
Stress is the internal force per unit area (N/m²); strain is the fractional change in length (ΔL/L), a dimensionless quantity. Stress carries pressure units, while strain has no units. The common mistake is writing strain with length units.
Memory trick: Stress = N/m², strain = ΔL/L (no unit).
“When a guitar string vibrates, the wave speed equals how fast the string wiggles times the distance between successive crests.”
Wave speed v equals frequency f times wavelength λ (v = fλ). Frequency sets how many cycles per second, λ sets the distance of one cycle, their product gives distance traveled per second. Trap: mixing up which quantity is given; always solve for the unknown, not assume v = λ/f.
v = fλ
Memory trick: v = fλ → ‘fast λ’
“A pot of water takes longer to boil than the same mass of oil on the stove.”
Specific heat c = Q/(mΔT) tells how much heat raises 1 kg by 1 °C; water’s c≈4.18 kJ/kg·K, much larger than metals, so water heats slowly. Remember to use mass in kg; using grams gives a 1000-fold error.
Q = mcΔT
Memory trick: c = Q÷(mΔT).
“Charging a metal sphere is like lifting a weight to a height; the work per unit charge is V = kQ/r.”
Electric potential at a point is the work done per unit positive charge in bringing it from infinity, V = kQ/r for a point charge. It is a scalar, so potentials add algebraically with sign. A common error is treating V as a vector and assigning direction.
V = kQ/r
Memory trick: V = work/charge; scalar, add with sign.
“Christmas lights in series dim each other, while parallel sockets each get full mains voltage.”
In series the same current flows through every element and total resistance adds (R_eq = ΣR); voltage divides among them. In parallel each branch sees the full source voltage and currents add (1/R_eq = Σ1/R). Trap: assuming current splits equally in series – it does not.
Memory trick: Series: I same, V splits; Parallel: V same, I splits
“A metal ring dropped through a strong magnet slows down as the induced current pushes back against its fall.”
The induced current creates a magnetic field that opposes the change in flux that produced it, conserving energy. The direction follows the right-hand rule, not the motion itself. Exams often ask for the direction; remember it always resists the flux change.
Memory trick: Lenz: induced emf tries to keep flux unchanged
“Like a fiber-optic cable guiding light around bends, TIR keeps the ray inside the glass beyond the critical angle.”
When light passes from a denser to a rarer medium, if the incidence angle exceeds the critical angle (θc = sin⁻¹(n₂/n₁)), the refracted ray would need sinθ>1, so it cannot propagate and the ray is reflected completely. This gives total internal reflection with 100 % efficiency. In exams remember: TIR only when n₁>n₂ and θi>θc; use the correct sign convention for angles measured from the normal.
Memory trick: Critical angle: sinθc = n₂/n₁ (lower over higher).