SI base units

“A scale (kg), ruler (m), stopwatch (s), fuse rating (A), thermometer (K), a 1 mol gas bottle, and a candle’s glow (cd) give the seven SI base units.”

The SI defines seven independent base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (thermodynamic temperature), mole (amount of substance), candela (luminous intensity). All other units are derived from them. A frequent trap is mixing candela (intensity) with lumen (flux) or treating kelvin as a temperature difference instead of absolute temperature.

Memory trick: My King Says A Knight Must Carry

Distance vs displacement

“Running one lap around a 400 m track, you travel 400 m distance but your displacement is zero because you end where you started.”

Distance is the total length of the path travelled; it is a scalar and never negative. Displacement is the straight-line vector from the initial to the final position; it can be zero or any direction. In questions, remember that distance adds up even on a return, while displacement may cancel.

Memory trick: Lap → distance adds, start-end same → displacement 0

Newton's first law (inertia)

“A parked bike stays still on a flat road until you give it a push.”

Newton’s first law says a body keeps its velocity—both speed and direction—when the net external force is zero, including the case of zero velocity (rest). The exam trap: uniform circular motion has constant speed but a centripetal force, so velocity changes and the law does not apply.

Memory trick: Zero net force → constant velocity (including zero)

Work done

“When you push a shopping cart straight ahead, the work you do equals the push force times the distance you move forward.”

Work is the component of force along the displacement multiplied by the distance: W = F d cosθ. If the force is perpendicular to motion, cosθ = 0 and work is zero. Exam trap: forgetting the cosθ factor when the force is at an angle.

W = Fd cosθ

Memory trick: W = F·d·cosθ → only the parallel part counts

Torque

“Turning a screwdriver to tighten a screw shows torque: the force at the handle creates a turning effect about the screw head.”

Torque τ = r F sinθ is the turning effect of a force about an axis. It equals the force magnitude times the perpendicular distance (r⊥ = r sinθ). The exam trap is to write τ = rF even when the force isn’t perpendicular, forgetting the sinθ factor.

τ = rF sinθ

Memory trick: τ = r × F⊥ → use the perpendicular component

Universal gravitation

“When you drop a pen, Earth pulls it with the same law that keeps the Moon circling us.”

Any two masses attract each other with force F = G m₁ m₂ / r², where G≈6.67×10⁻¹¹ N·m²/kg². The distance r is measured between the centres of the masses. Exam trap: using surface separation instead of centre-to-centre distance.

F = Gm₁m₂/r²

Memory trick: G = 6.67 → think ‘6.6-7-7’ as a lucky number

Pressure in a fluid

“When you dive into a swimming pool, the deeper you go, the heavier the water above pushes on you.”

Pressure at depth follows P = P₀ + ρgh: surface pressure plus weight of fluid column. ρ is fluid density, g is gravity, h is depth. Remember gauge pressure excludes atmospheric P₀; exam often asks for increase only, so use ΔP = ρgh.

P = P₀ + ρgh

Memory trick: ΔP = ρ·g·h → 'Pushes (ρ) Gently (g) Higher (h)'

Hooke's law

“A kitchen scale’s spring stretches linearly until the needle’s movement deviates from a straight line.”

Hooke’s law gives σ = E·ε only up to the proportional limit, where the σ–ε graph is a straight line. The elastic limit is the maximum stress that still yields completely reversible strain and may lie beyond the proportional limit. The yield point is where permanent deformation begins; confusing elastic and proportional limits costs marks.

stress ∝ strain

Memory trick: Proportional = straight line; Elastic = full return; Yield = first permanent bend.

Simple harmonic motion

“A spring in your pen holder pulls back exactly as far as you stretch it.”

In SHM the restoring force is proportional to displacement and opposite in direction, giving F = –kx. This linear relation makes the motion sinusoidal. Exam trap: missing the negative sign when writing the equation of motion.

F = −kx

Memory trick: Force = -k × displacement → ‘-k’ like ‘negative kick back’

Temperature vs heat

“When you touch a hot iron, the burn you feel is the iron’s heat flowing into your skin, not the iron’s temperature itself.”

Temperature measures the average kinetic energy of molecules; it is a state function and does not depend on the system size. Heat is energy that flows between bodies when there is a temperature difference; it is not a property of a single body. In calculations, use Q for heat transfer, not ΔT.

Memory trick: Temp = how hot; Heat = how much energy moves.

Coulomb's law

“When two balloons rubbed on hair push each other apart, the repulsive force follows F = kq₁q₂/r².”

The electrostatic force between two point charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance. k = 1/(4πϵ₀) provides the correct units. Remember: opposite signs attract, like signs repel, and never drop the r² in the denominator.

F = kq₁q₂/r²

Memory trick: Like gravity, but sign matters: F ∝ q₁q₂ / r².

Ohm's law

“A garden hose shows Ohm’s law: higher water pressure (voltage) drives more flow (current) if the hose’s resistance stays the same.”

For an ohmic conductor at constant temperature, V and I are directly proportional: V = IR. The resistance R stays constant, so doubling V doubles I. Exam trap: many materials (filaments, semiconductors) are non-ohmic, so verify linear V-I behavior before applying the law.

V = IR

Memory trick: V ∝ I → V=IR, like pressure = flow×restriction

Force on a moving charge

“A charged particle curves like a car turning on a road when it enters a magnetic field.”

A magnetic field exerts a force F = q v B sinθ on a charge moving with velocity v at angle θ to the field. The force is perpendicular to both v and B, causing circular or helical motion. In exams, remember the force vanishes when motion is parallel or antiparallel to the field (θ = 0° or 180°).

F = qvB sinθ

Memory trick: F = qvB sinθ → ‘Force = charge × velocity × B × sinθ’

Laws of reflection

“When you look into a calm lake, the angle your line of sight makes with the water equals the angle the reflected ray makes back to your eye.”

The incident ray, reflected ray and the normal lie in the same plane, and ∠i = ∠r. This holds for any smooth surface. In problems, remember to take the normal direction correctly; the angle is measured from the normal, not the surface.

Memory trick: Incidence = Reflection, measured from the normal.

Photoelectric effect

“A UV black-light on a zinc plate ejects electrons, while a red torch of the same brightness leaves the metal unchanged.”

A photon ejects an electron only if its energy hν meets or exceeds the metal work function φ; the excess appears as kinetic energy K = hν−φ. Raising light intensity raises the photon count, so the photocurrent grows, but K stays set by frequency alone. The common trap is assuming more intense light can increase K or that any light eventually frees electrons.

Memory trick: hν≥φ → K=hν−φ; intensity ↑ → more electrons, not more KE.

Electromagnetic waves

“Your Wi-Fi router sends invisible waves that zip through the air at 3×10⁸ m/s, just like light.”

An electromagnetic wave is a pair of perpendicular electric (E) and magnetic (B) fields that regenerate each other while moving at c = 3×10⁸ m/s. No material medium is required because the changing fields sustain the wave. Exam trap: forgetting that all EM waves travel at the same speed in vacuum.

c = 3×10⁸ m/s

Memory trick: E ⟂ B ⟂ direction, all travel at c

Resolving a vector into components

“When you aim a smartphone’s compass arrow, its northward and eastward parts are the x-y components.”

A vector can be replaced by perpendicular x- and y-components whose sum reproduces the original arrow. If the vector makes angle θ with +x, Ax = A cosθ and Ay = A sinθ; assign signs from the actual direction. Forgetting sign when the angle is measured from the negative axis is a common trap.

Memory trick: Cos = adjacent, Sin = opposite – assign sign after drawing.

Heat versus temperature

“When you heat a cup of tea, the steam rises because heat flows from the hot tea to the cooler air.”

Temperature measures the average kinetic energy of particles; heat is energy transferred because of a temperature difference. Heat always flows from higher to lower temperature. In problems use Q = mcΔT for sensible heat, never treat temperature itself as energy.

Memory trick: Hot → cold = heat flow; T drives, Q transfers

Microscopic origin of gas pressure

“Like ping-pong balls repeatedly bouncing off a box wall, each hit pushes the wall and creates pressure.”

Gas pressure equals the total momentum transferred to the wall per unit area per unit time. Each molecular collision changes momentum; more frequent or harder hits raise pressure. Trap: treating pressure as an intrinsic property of the gas rather than wall interaction.

Memory trick: Pressure = hit-rate × momentum-change per hit ÷ area

Potential as energy per charge

“The voltage shown on a phone charger tells how much energy each coulomb of charge carries.”

Electric potential at a point equals the potential energy of a test charge divided by its magnitude. It is a scalar, so contributions from many source charges add algebraically, keeping their signs. Forgetting the sign or treating V as a vector leads to wrong answers.

Memory trick: V = PE/q, scalar → add with signs

Magnetic dipole moment

“When you hold a compass, its needle aligns because its dipole moment runs from the hidden south pole to north, like a tiny bar magnet.”

The magnetic dipole moment vector of a bar magnet points from its internal south pole toward its north pole. In a uniform external field B the torque is τ = m × B, which tries to align m with B. A common trap is using the external field line direction (north to south) as the moment direction, which reverses the sign of the torque.

Memory trick: Moment S→N inside; τ = m×B aligns m with B.

Rutherford scattering and nuclear atom

“Like a bullet passing through a fishing net, most go straight while a few get caught on a knot.”

Most α particles travel straight because an atom is mostly empty space; only a tiny fraction are sharply deflected, revealing that the positive charge and most of the mass reside in a very small nucleus. The exam trap is to think all particles are equally scattered.

Memory trick: Most pass, few bounce → nucleus is tiny.

Nuclear size and density

“A gold nucleus feels like a marble; doubling nucleons only makes its radius grow by the cube-root, not double.”

Nuclear radius R = R₀ A^(1/3). Since volume ∝ A and mass ∝ A, density ρ ≈ constant (~2.3×10¹⁷ kg m⁻³) for all nuclei. The trap is to forget the cube-root and assume linear growth.

Memory trick: R ∝ A^(1/3) → cube-root rule

Least count and instrument reading

“Reading a vernier caliper is like counting the treads on a ladder; you can’t see steps smaller than one tread.”

An instrument cannot resolve changes smaller than its least count. The true reading = main-scale reading + (coinciding division × least-count) – zero-error (sign as given). Forgetting the sign or the least-count term gives a wrong value, a frequent loss-mark.

Memory trick: LC = smallest tick; reading = MSR + CD·LC – ZE.