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
“When a diver blows a whistle underwater, the tone you hear is the same pitch as in air, but the sound’s wavelength is longer because water lets it travel faster.”
Frequency is set by the source and does not change when the wave passes into another medium. Since v = f λ, λ = v/f, a higher speed in the new medium makes λ larger. Forgetting that f stays constant is a common trap.
Memory trick: f fixed → λ follows v
“In a cathode-ray tube, the glowing electron beam bends sideways just like a kite pulled by a cross-wind.”
A charge q moving with velocity v in a magnetic field B experiences a force F = q(v × B). The force is perpendicular to both v and B, so it only changes direction, never speed, and does no work. If v is parallel to B, the perpendicular component is zero and the force vanishes.
Memory trick: Only v⊥B counts – if parallel, F=0
“A laser pointer split by a beam-splitter produces stable fringes because both beams originate from the same source.”
Two sources are coherent when the phase difference between them remains constant in time. This constant phase ensures a fixed interference pattern. In exams, remember that separate lamps are not coherent; only one source divided into two beams works.
Memory trick: Coherent = constant phase (one source → two beams).
“When you turn the dial on a crystal radio, the capacitor’s reactance shrinks as the station’s frequency rises.”
Reactance is the opposition offered by a capacitor (Xc = 1/ωC) or an inductor (XL = ωL) to alternating current. Unlike resistance, it varies with the signal’s angular frequency ω. A common exam error is to treat Xc or XL as a constant resistance.
Memory trick: Xc ∝ 1/ω, XL ∝ ω → “C down, L up” with frequency.
“A diode in a flashlight glows when the battery’s positive is connected to the p-side, but stays dark if reversed.”
In forward bias the external voltage reduces the built-in potential, narrowing the depletion layer so carriers cross and current flows. In reverse bias the applied voltage adds to the barrier, widening the depletion region and essentially stopping current (only a tiny leakage). Exam trap: forgetting that reverse bias still allows a micro-ampere leakage, not zero.
Memory trick: Forward: p→+, n→− = ‘push forward’; Reverse: swap = ‘stop’.
“A runner’s speed on the track reads 12 km/h, but his displacement arrow on the map also points north.”
A scalar has only magnitude (e.g., mass, temperature, speed); a vector has magnitude and a specific direction (e.g., displacement, velocity, force). Vectors obey the parallelogram rule and can be added tip-to-tip. A common trap is confusing speed with velocity – the latter is a vector.
Memory trick: If direction matters, it's a vector
“A car cruising at steady speed on a highway covers equal miles every minute, just like uniform motion.”
Uniform motion has constant velocity, so the x–t graph is a straight line with constant slope and acceleration = 0. In non-uniform motion the slope varies, giving a curved x–t graph and non-zero acceleration. Trap: many forget that a straight-line x–t graph also guarantees zero acceleration, not just a flat v–t line.
Memory trick: Uniform = straight-line x-t; non-uniform = curved x-t
“When you push a shopping cart, the harder you push, the faster it speeds up.”
Net force equals the time rate of change of momentum; for constant mass it simplifies to F = ma. It tells how acceleration scales with applied force and mass. Beware mixing mass (kg) with weight (N); use m, not mg, in the formula.
F = ma
Memory trick: F = m·a, not weight.
“A baseball thrown at 30 m/s carries four times the kinetic energy of the same ball at 15 m/s.”
Kinetic energy of a mass m moving at speed v is KE = ½ m v²; it grows with the square of speed. The ½ factor is essential. Common mistake: using KE = m v² or omitting the square of velocity.
KE = ½mv²
Memory trick: KE ∝ v², double v → 4× KE
“A figure skater’s arms outstretched feel a larger moment of inertia, making spins slower.”
I = Σmr² sums each mass element times the square of its distance from the rotation axis, reflecting resistance to angular acceleration. Mass farther away contributes disproportionately because of the r² factor. The common exam slip: forgetting to square the distance or ignoring axis shift.
I = Σmr²
Memory trick: I ∝ distance² – far mass weighs more
“A sky-diver 10 km above ground feels 99.7 % of the surface gravity, showing g hardly changes over a few kilometres.”
At a planet’s surface g = GM/R². For an altitude h replace R by (R+h): g = g0·(R/(R+h))², so g drops as the inverse square of distance. Inside a uniform-density Earth g = g0·r/R, vanishing at the centre. A common mistake is to use surface g for satellites or deep-earth problems without adjusting the distance.
g = GM/R²
Memory trick: Double distance → g¼; inside uniform Earth g ∝ r.
“Pressing the brake pedal makes the fluid in brake lines push equally on all brake shoes.”
Pascal's law states that a change in pressure applied to an enclosed incompressible fluid is transmitted undiminished in all directions. Pressure stays same, but force = pressure × area, giving mechanical advantage. Trap: never add forces, only pressures.
Memory trick: Equal pressure, equal push
“A steel ruler bends less than a rubber ruler under the same weight because its Young’s modulus is higher.”
Young’s modulus Y = stress/strain quantifies stiffness; a larger Y means a material deforms less under a given stress. It is the slope of the linear stress-strain curve in the elastic region. Trap: confusing Y with bulk modulus or using inconsistent units.
Y = stress/strain
Memory trick: Y = slope of σ-ε line; high Y = stiff.
“A playground swing’s swing time depends only on how long the chain hangs, not on your weight.”
For a simple pendulum of length L, period T = 2π√(L/g). Mass cancels out and small amplitudes keep the approximation valid. Trap: using the formula for large amplitudes where the period slightly increases.
T = 2π√(L/g)
Memory trick: T ∝ √L → ‘T swings with √L’
“A railway track bows slightly on a sunny day because the steel rails expand with heat.”
Heating raises molecular vibration, increasing average separation, so most solids expand (positive α). Free expansion: ΔL = αL₀ΔT. If the body is constrained, length may not change but stress develops – a common exam nuance.
Memory trick: Hot → longer, cold → shorter.
“A positively charged comb makes tiny hair strands stand up, showing the field E = F/q pointing away from the comb.”
Electric field is the force on a positive test charge per unit charge, E = F/q. Field lines start on + charges and end on – charges and cannot cross because a point cannot have two directions. The exam trap: using the direction for a negative test charge without reversing it.
E = F/q
Memory trick: E points away from +, toward –; lines never cross.
“A long, thin wire in a toaster gets hotter than a short, thick one because its resistance is larger.”
Resistance is given by R = ρL/A; it rises with length L and material resistivity ρ, and falls with larger cross-sectional area A. High-ρ materials (nichrome) resist more. Trap: forgetting that A is in the denominator, leading to R ∝ A error.
R = ρL/A
Memory trick: Long & thin → high R; short & thick → low R
“When you push a magnet into the coil of a bike dynamo, the headlamp flickers because the magnetic flux is changing.”
A time-varying magnetic flux through a loop induces an emf given by EMF = –dΦ/dt. The negative sign shows the induced emf opposes the change (Lenz’s law). Only a changing flux, not a static one, produces emf – a common exam slip.
EMF = −dΦ/dt
Memory trick: EMF ∝ rate of flux change – faster push, bigger spark
“A straw appears bent at the water surface because light changes speed, obeying n₁sinθ₁ = n₂sinθ₂.”
At a planar interface, n₁ sinθ₁ = n₂ sinθ₂, where n = c/v. Light bends toward the normal when entering a higher-index medium. The trap: use the normal as reference for both angles; mixing surface-measured angles gives wrong results.
n₁sinθ₁ = n₂sinθ₂
Memory trick: n sin θ constant across boundary.
“A blue laser pointer’s photons carry more energy than a red one, even though both have the same brightness.”
Each photon carries energy E = hf = hc/λ; higher frequency (shorter λ) means a more energetic photon. Brightness (intensity) only changes photon count. Trap: mixing intensity with photon energy.
E = hf
Memory trick: E ∝ 1/λ; shorter colour = higher photon bite.
“When you tune a radio, you’re catching the longest waves; as you move to X-rays in a hospital, the waves get dramatically shorter.”
From longest to shortest wavelength the order is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Energy ∝ 1/λ, so shorter waves carry more energy. Trap: mixing up UV and X-ray positions—X-rays sit just before gamma.
Memory trick: R-M-I-V-U-X-G (Radio to Gamma)
“Like a GPS showing eastward distance even when you drive west, forgetting sign flips the vector.”
The magnitude formulas give only absolute values; the sign must come from the arrow’s direction. When the vector points left or down, the corresponding component is negative. Ignoring this leads to a wrong resultant.
Memory trick: If arrow points left/down, make that component negative.
“A refrigerator’s compressor removes heat while the interior stays colder, showing heat and temperature are distinct.”
Temperature is a state property; heat is a path-dependent transfer. Confusing them flips sign conventions and gives wrong Q values. Keep heat lost negative and heat gained positive, or use the signed-heat equation consistently.
Memory trick: T is state, Q is transfer – keep signs separate
“Imagine a balloon’s pressure as invisible gas weight; actually it’s the rapid hits of molecules on the balloon skin.”
Pressure is not a stored substance inside the gas; it arises from continual molecular impacts on the container surface. The wall feels equal and opposite momentum change. Trap: visualising pressure as a fluid-like “stuff” inside the gas.
Memory trick: Pressure = hits on wall, not gas “stuff”