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
“A runner’s split-second speed on a stopwatch is not the same as the average speed over the whole lap.”
Average velocity = total displacement ÷ total time, while instantaneous velocity is the limit as the time interval approaches zero. Using Δs/Δt for a finite interval gives the average, not the instant.
Memory trick: Avg = Δs/Δt; instant = limit Δt→0
“A hockey puck glides on smooth ice, staying at constant speed until a stick hits it—showing inertia.”
Inertia is the resistance of any mass to a change in its state of rest or uniform motion, as stated in Newton’s first law. It is not a force; it is proportional to mass. A frequent error is to think a force is needed to keep an object moving; only a net external force changes its motion.
Memory trick: Inertia ∝ mass, no force needed to stay moving.
“Carrying a heavy bag straight across a room does no work against gravity because the force is vertical while displacement is horizontal.”
When the applied force is perpendicular to the displacement, cosθ = 0, so work is zero. Students often count the effort of holding a weight as work, but work measures energy transferred, not mere effort. Remember: only the force component along the motion does work.
Memory trick: Perp force → cos90°=0 → W=0
“A bowling ball rolling down the lane carries both forward speed and spin, giving it extra kinetic energy.”
A rolling object has translational kinetic energy ½mv² and rotational kinetic energy ½Iω². Both must be added for the total kinetic energy. A frequent slip is to count only the translational part or to misuse v = ωr for a slipping case.
Memory trick: KE = ½mv² + ½Iω² → ‘half m v² plus half I ω²’
“A satellite 10 Rₑ from Earth has PE = –GMm/(10Rₑ), far below the zero set at infinity.”
Gravitational potential energy of a mass m at distance r from Earth’s centre is U = –GMm/r, zero at infinity. Near Earth this reduces to mgh, but for satellites the –GMm/r form must be used. Mistake: applying mgh at large r.
Memory trick: PE negative, zero at ∞; use –GMm/r.
“Airplane wings generate lift as air moves faster over the curved top, creating lower pressure there.”
Bernoulli’s equation states P + ½ρv² + ρgh = constant along a streamline for steady, non-viscous, incompressible flow. Hence, where the fluid speed is higher the pressure is lower. Misuse occurs when height changes are ignored or when the flow is viscous or turbulent.
P + ½ρv² + ρgh = constant
Memory trick: Fast = low pressure (Bernoulli).
“When you pull a rubber tube, it gets thinner; the ratio of that thinning to the stretch is the Poisson ratio.”
Poisson’s ratio ν = –(lateral strain)/(longitudinal strain). The negative sign makes ν positive for most materials, which contract laterally when stretched longitudinally. Typical metals have ν ≈ 0.3; ν cannot exceed 0.5 for isotropic elastic solids.
Memory trick: ν = –Δwidth/Δlength
“A flute (open at both ends) can play every note, while a clarinet (closed at one end) skips even notes.”
Open pipe: λ = 2L/n → all integer harmonics. Closed pipe: λ = 4L/(2n-1) → only odd harmonics. The error is applying the open-pipe formula to a closed pipe, giving a nonexistent even harmonic.
Memory trick: Closed = odd only; Open = all
“A gas compressed in a piston feels hotter, but its internal energy rise is due to temperature increase, not pressure itself.”
In an ideal gas internal energy is a function of temperature alone; pressure or volume changes do not affect U directly. Assuming ΔU ∝ ΔP or ΔV is a frequent error. Remember: if temperature stays the same, ΔU = 0.
Memory trick: ΔU = 0 if T constant (ideal gas)
“Climbing a hill feels the height (potential) while wind blowing shows direction (electric field) – one is scalar, the other vector.”
Electric field E is a vector defined as force per unit positive charge, E = F/q, and points from positive to negative charges; electric potential V is a scalar, the work per unit charge, V = -∫E·dl. Trap: using V where E is needed, or treating E as a scalar.
Memory trick: E = arrow, V = height – different types.
“A thin straw sips slower than a thick pipe; similarly, thin wire has higher resistance than a thick one.”
Resistance R = ρ L/A; ρ is the material’s intrinsic resistivity, unchanged by shape. Increasing length raises R, increasing cross-section lowers R. The exam pitfall is mixing up resistivity (material property) with resistance (geometric). Cutting a wire changes R but not ρ.
Memory trick: R ∝ L, ∝ 1/A; ρ stays same
“Moving a magnet through a loop is like shaking a bottle; the liquid (charge) rushes out only while the shaking (flux change) continues.”
Faraday’s law: a changing magnetic flux Φ through a circuit induces an emf ε = –dΦ/dt (or ε = –N dΦ/dt for N turns). Only a change in field strength, area, or orientation produces emf; a steady flux gives none. The negative sign reflects Lenz’s law and is a frequent source of sign errors.
Memory trick: Faraday: EMF = –ΔFlux/Δt → need change, not static.
“A 12-g block of pure carbon-12 contains exactly 6.022×10²³ carbon atoms.”
Avogadro’s number N_A = 6.022×10²³ particles per mole. One mole of any substance holds this many entities, tying the macroscopic gram scale to the atomic scale. Use N_A for mole-to-particle conversions; do not round to 6×10²³ in precise stoichiometry.
N_A = 6.022×10²³
Memory trick: 12 g C-12 = N_A atoms
“Your kitchen scale reading 44 g of CO₂ equals one mole because its molar mass (44 g mol⁻¹) matches the molecular weight.”
Molar mass (M, g mol⁻¹) is the mass of one mole and numerically equals the atomic/molecular mass in amu. Use n = m/M to find moles. Trap: mixing up units – treat M as g mol⁻¹, not as amu, before using the formula.
n = m/M
Memory trick: M (g/mol) = atomic mass (u) × 1 g/u
“Glucose’s sweet formula C₆H₁₂O₆ is six times its simplest ratio CH₂O, like a LEGO set built from the basic CH₂O block.”
Empirical formula gives the lowest whole-number atom ratio; molecular formula = integer multiple of empirical. Find the factor k = (molar mass)/(empirical mass). Trap: assuming empirical = molecular without checking the molar mass.
Memory trick: Molecular = Empirical × (M_molar ÷ M_empirical)
“A soda bottle containing 0.5 mol of CO₂ in 0.25 L gives a Molarity of 2 M, like a concentrated juice concentrate.”
Molarity M = n/V (mol L⁻¹) uses total solution volume, not just solvent. Temperature changes V, so M changes. Trap: using solvent volume or forgetting to convert mL to L.
M = n/V
Memory trick: M = moles ÷ litres of solution
“In a firecracker, the limited amount of black-powder determines the maximum bang, no matter how much fuse you add.”
Convert each reactant to moles and compare with stoichiometric coefficients; the reactant giving the smallest possible product amount is the limiting reagent. Trap: ignoring the coefficient when judging which is limiting.
Memory trick: Limiting = smallest (moles ÷ coefficient)
“Like a positively charged balloon (protons) pulling tiny negatively charged confetti (electrons) around it, while neutrons sit quietly inside.”
Atoms consist of a nucleus containing positively charged protons and neutral neutrons, surrounded by negatively charged electrons in shells. The opposite charge of protons and electrons holds the atom together, while neutrons add mass without affecting charge. Exam trap: mixing up neutron charge as negative.
Memory trick: P+ N0, E− : Proton positive, Neutron zero, Electron negative.
“A school class roll number (Z) tells who you are, while the total number of students plus teachers (A) tells the class size.”
Atomic number Z equals the number of protons and uniquely identifies an element. Mass number A is the sum of protons and neutrons (A = Z + N) and approximates the atom’s mass in atomic mass units. Trap: treating A as the exact atomic mass or forgetting it is an integer count.
A = Z + N
Memory trick: Z = ID, A = heads (protons+neutrons).
“Identical twins (same protons) wearing different weight belts (neutrons) are still the same person.”
Isotopes are atoms with the same Z (same element) but different numbers of neutrons, giving different mass numbers. Chemical behavior remains nearly identical because electrons see the same nuclear charge, while nuclear stability can vary. Trap: assuming isotopes change chemical reactivity.
Memory trick: Same Z, different N → isotopes.
“An apartment address: building (n), floor (l), door (m), and whether the light is on (s) uniquely locates an electron.”
Four quantum numbers (n, l, m, s) uniquely label an electron: n sets the energy shell, l the subshell shape, m the orbital orientation, and s the spin (+½ or –½). Together they obey specific ranges (l < n, m = –l…+l). Trap: assigning m values outside –l to +l or forgetting spin can cause invalid configurations.
Memory trick: n-l-m-s = building-floor-door-switch.
“When filling a parking lot, cars park in the nearest empty spot before moving to farther rows.”
The Aufbau principle orders electron filling by increasing (n+ℓ) value; if two orbitals share the same (n+ℓ), the one with lower n fills first. This explains why 4s fills before 3d. Trap: ignoring the (n+ℓ) rule leads to wrong configurations like placing 3d before 4s.
Memory trick: Fill by smallest (n+ℓ), then lower n.
“A restroom stall can hold at most two people, and they must wear opposite-colored socks (spins).”
Pauli’s exclusion principle states that no two electrons in an atom can have identical sets of all four quantum numbers; thus an orbital can accommodate at most two electrons, which must have opposite spins (+½, –½). This limits electron pairing and shapes the periodic table. Trap: assuming two electrons can share the same spin in one orbital.
Memory trick: One orbital = 2 electrons, opposite spins.
“When you seat people at a round table, you first give each a seat before anyone sits next to another.”
Electrons fill degenerate orbitals singly with parallel spins to maximize total spin (exchange energy). This lowers electron repulsion. In JEE/NEET, pairing starts only after every orbital of the subshell has one electron; missing this gives wrong configurations.
Memory trick: Hund → one each before pair, same spin