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
“Like a rolling dice, a monatomic gas molecule can move independently along x, y, z – three translational freedoms.”
A degree of freedom (DoF) is an independent quadratic term in a molecule’s kinetic energy. Translational DoF =3 for all gases; linear molecules add 2 rotational, non-linear add 3. Vibrational DoF become active only when temperature is high enough to excite them.
Memory trick: 3T + (2R linear /3R non-linear) + active V
“Bringing the plates of a parallel-plate capacitor closer is like squeezing a sandwich tighter; the same area stores more charge.”
Capacitance C = Q/V is a property of the conductor’s geometry (area, separation) and the dielectric constant, not of the particular charge or voltage. Changing Q and V together leaves C unchanged; only A, d or ε affect it. The exam trap is to think C grows when you add charge to a fixed capacitor.
Memory trick: C = ε·A/d → larger A or smaller d gives larger C.
“A compass needle (ferromagnet) snaps to Earth’s field, while a glass beaker of water (diamagnet) barely pushes away a strong magnet.”
Diamagnets (χ<0) develop a minute moment opposite to the field, causing weak repulsion. Paramagnets (χ>0, small) align partially with the field, giving a weak attraction. Ferromagnets contain spontaneously aligned domains; they show strong attraction and retain magnetisation; the exam trap is to assume any attracted material is ferromagnetic—look at χ magnitude or hysteresis.
Memory trick: D-P-F: Repel, Attract, Fixed domains.
“When a hydrogen discharge tube glows, each color is from electrons falling to the same lower level, defining a spectral series.”
All transitions ending on the same lower level n_f make a series; photon energy is E = 13.6 eV (1/n_f² − 1/n_i²) for emission (n_i>n_f). A frequent mistake is interchanging n_i and n_f, which flips the sign and yields an impossible negative energy.
Memory trick: Lyman-1, Balmer-2, Paschen-3 – lower-level number.
“Like popcorn kernels popping, you never know which one will pop, but half of a big batch pop in a given time.”
Half-life is the time for half of a large ensemble of identical nuclei to decay. It reflects a probability, not a fixed timer for each atom. The trap is applying the ½ rule to a small sample or to a single nucleus.
Memory trick: Half-life = statistical half, not a personal timer.
“When you weigh a mango on a kitchen scale showing 150.2 g, you can’t claim the weight is 150.200 g.”
A result must not show more significant figures than the least precise measurement. In multiplication or division the answer keeps the same number of sig-figs as the factor with the fewest; in addition or subtraction it keeps the same number of decimal places as the term with the fewest. The classic trap is rounding after every step – keep guard digits and round only once at the end.
Memory trick: Mul/Div → min sig-figs; Add/Sub → min decimal places; round only once.
“When two guitar strings are slightly out of tune, the sound swells and fades at the beat frequency.”
The beat frequency equals the absolute difference of the two close frequencies: f_beat = |f1-f2|. It arises because the amplitudes add and cancel periodically. The common mistake is to take f1+f2; only the difference produces the audible pulsation.
Memory trick: Beat = |higher – lower|
“Running a loop of wire around a straight current-carrying wire lets the magnetic field you feel along the loop sum to μ0 I.”
Ampere’s circuital law states ∮ B·dl = μ0 I_enc. The line integral equals μ0 times the net current piercing the loop. Only when the geometry makes B uniform (e.g., infinite straight wire, solenoid) can you replace the integral by B·l; otherwise the full integral must be evaluated.
Memory trick: ∮B·dl = μ0 I_enc → ‘B around = μ0 I inside’
“When a laser passes through two tiny slits, the bright spots on the screen are spaced by β = λD/d.”
β is the fringe width in Young's double-slit experiment. It follows from the small-angle approximation (sinθ≈tanθ≈β/D) with slit separation d and screen distance D. The formula fails if D is not much larger than d or angles are large, so always check the geometry before applying it.
β = λD/d
Memory trick: Big λ or big D → wide β; small d → wide β.
“Turning the AM-radio knob varies a capacitor, moving the station’s frequency set by f = 1/(2π√LC).”
The formula f = 1/(2π√LC) gives the natural frequency of an ideal loss-less LC circuit. It holds for both series and parallel resonance when resistance is negligible. In a real RLC circuit the resonance frequency shifts slightly; using the formula with a large R leads to error.
f = 1/(2π√LC)
Memory trick: LC → f = 1/(2π√LC) (One over two-pi root LC)
“A diode is like a one-way turnstile: conventional current can only pass from the anode side into the cathode side.”
When V_A-C = V_anode−V_cathode >0 (forward bias) the junction barrier collapses and the diode conducts. With V_A-C <0 (reverse bias) the barrier widens, allowing only a tiny leakage; appreciable reverse current appears only at the breakdown (Zener) voltage. The common trap is writing “V>0” without the A-C reference, which can flip the bias condition.
Memory trick: Forward = A-C positive; Reverse = stop (unless Zener).
“When checking the formula for kinetic energy, you verify that (kg·m²/s²) matches the dimensions of energy, just like confirming a recipe’s units before cooking.”
Dimensional analysis rewrites every quantity as powers of mass (M), length (L) and time (T). It guarantees that both sides of an equation have identical dimensions, catching algebraic slips. The trap: a dimensionally correct expression can still be numerically wrong if a dimensionless constant is missing, so always verify constants separately.
Memory trick: M L T powers must match on both sides.
“A cricketer bowls a ball and sees it travel farthest when released at about 45° to the ground.”
For a projectile launched from and landing on the same level, the range R = u²·sin2θ/g. Since sin2θ peaks at 1 when 2θ=90°, the maximum range occurs at θ=45°. This holds only without air resistance and with equal launch-landing heights; otherwise the optimal angle shifts.
R = u²sin2θ/g
Memory trick: Max range → sin2θ=1 → θ=45°
“A stone tied to a string whirls in a circle, and the string’s pull is the inward force that keeps it from flying away.”
A body moving in a circle of radius r with speed v needs a net inward force F = mv²/r. This force can be tension, gravity, or normal reaction; it is not a new type of force. The trap: forgetting that the direction is always toward the centre, not along the velocity.
F = mv²/r
Memory trick: Centripetal = Center Pull.
“A compressed spring in a toy car stores energy that later launches it forward.”
The energy stored in a spring displaced by x from its natural length is PE = ½ k x², where k is the spring constant. It equals the work done on the spring and is fully recoverable in an ideal spring. Trap: using ½ k x instead of x² gives wrong units.
PE = ½kx²
Memory trick: ½ k x² – half-k times square of stretch
“On a playground merry-go-round, pulling the seats inward makes it spin faster because the mass moves nearer the axis, lowering I.”
I = Σ m r², so the same body has different moments about different axes. For a solid disc (M,R) I = ½ MR², while a thin hoop of the same M,R has I = MR². A trap is forgetting to add MR² when the axis is shifted to the rim (parallel-axis theorem).
Memory trick: I ∝ r² → remember ‘far-far-far’ (distance squared).
“If the Moon were twice as far from Earth, its pull would drop to one-quarter.”
The gravitational force follows an inverse-square law: doubling the separation makes the force 1/4, tripling makes it 1/9. A common error is to think the force halves when distance doubles. Remember to square the distance factor.
Memory trick: Double distance → quarter force.
“A rubber duck in a bathtub pushes down water; the water pushes up with a force equal to the weight of water displaced.”
Archimedes principle states that any body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. The force depends on the displaced volume and fluid density, not on the object's own weight. A common trap is using the object's density instead of the fluid's when calculating the force.
Memory trick: Buoyancy = ρ_fluid × V_displaced × g
“A steel rod feels harder to stretch than a rubber band because steel’s Young’s modulus is much larger.”
A larger modulus indicates a stiffer material, not easier deformation. Young’s, bulk and shear moduli quantify resistance to length, volume and shape changes respectively. The trap: confusing high modulus with high ductility; high modulus means low strain for a given stress.
Memory trick: Stiff = big modulus, not soft
“Feel the echo in a warm kitchen; the sound returns quicker than in a cold cellar.”
Speed of sound v = √(γRT/M) ≈ 331 + 0.6 T°C m/s, so it rises about 0.6 m/s per °C. Many forget the temperature term and use 343 m/s for all conditions.
Memory trick: v≈331+0.6 T°C (m/s)
“When you inflate a bicycle tyre, the pressure rises as you pump more air at the same temperature.”
For an ideal gas, pressure, volume and temperature obey PV = nRT, derived from kinetic theory of non-interacting point particles. The relation holds only when temperature is in kelvin; using °C is a common source of error.
PV = nRT
Memory trick: K = °C + 273; use K
“A water molecule’s bent shape makes it act like a tiny bar of + and – charges separated by a few angstroms.”
Two equal and opposite charges ±q a short distance 2a form an electric dipole. Dipole moment p = q·2a points from negative to positive; its field at distance r (r≫a) falls as 1/r³ (∝ (p/r³)(2cosθ r̂+sinθ θ̂)). In exam questions, using the 1/r² monopole law is a common trap—remember the far-field of a dipole is 1/r³.
p = q×2a
Memory trick: p = q×2a → ‘double-a’ for dipole
“A Wheatstone bridge is like a playground seesaw with two pairs of kids; when the weight ratios match, the middle pivot (galvanometer) feels no push.”
In a Wheatstone bridge, balance occurs when the ratio of the two resistors in one branch equals that in the other: R1/R2 = R3/Rx. At this point the galvanometer carries zero current, so its resistance does not affect the condition. A common mistake is to think the galvanometer resistance changes the balance equation; it does not.
Memory trick: Balance: R1·Rx = R2·R3
“The needle of a compass sways when a tiny current flows through the coil, just like a tiny motor.”
A moving-coil galvanometer has a rectangular coil suspended in a uniform magnetic field. Current I produces torque τ = N I A B, rotating the coil and deflecting the pointer. Deflection is proportional to I, so it measures small currents. Trap: the scale is linear only while the spring restoring torque remains linear; beyond that it saturates.
Memory trick: I → coil torque → pointer deflection