Venturi meter

“When you squeeze a garden hose nozzle, the water jets faster and the pressure at the throat drops, just like a Venturi meter.”

Continuity gives v2 = v1·A1/A2. Bernoulli then yields Δp = ½ρv1²[(A1/A2)²−1]. Solving for discharge gives Q = C_d·A2·√[2Δp / (ρ(1−(A2/A1)²))]. The trap is forgetting the (1−(A2/A1)²) term or omitting the discharge coefficient, which inflates the flow rate.

Memory trick: Cd·A2·√(2Δp /[ρ(1−(A2/A1)²)]) – keep the ‘1-minus-ratio-squared’ denominator.

Independent horizontal and vertical motion

“Like a basketball’s horizontal drift while gravity pulls it down, each follows its own clock.”

Horizontal motion has zero acceleration, so v_x = u cosθ stays constant; vertical motion has a-g, giving y = u sinθ t – ½gt². Both use the same time variable, so the projectile’s path is found by solving the two equations together. A mistake is to let the vertical acceleration affect v_x.

Memory trick: One t, two eqns: x = u cosθ t, y = u sinθ t – ½gt².

Thermal expansion

“On a scorching summer, railway tracks lengthen and may buckle if the expansion isn’t restrained.”

Heating increases average inter-atomic spacing, giving linear expansion ΔL = αLΔT. For isotropic solids, area expands ≈2α and volume ≈3α when α is small. Trap: using α directly for area/volume without the factor 2 or 3.

Memory trick: Area≈2α, Volume≈3α

Temperature and molecular kinetic energy

“A thermometer’s mercury rises because molecules, regardless of mass, carry the same average kinetic energy at that temperature.”

For an ideal gas, ⟨KE⟩ = 3k_B T/2, independent of molecular mass. Hence lighter molecules have higher rms speed at the same T. Trap: mixing up average kinetic energy with speed; heavy gases move slower even though ⟨KE⟩ is equal.

Memory trick: KE_avg = 3kT/2 – mass-free

Field-potential relationship

“Water flowing downhill mirrors a positive charge moving from high to low potential.”

The electric field points toward the direction of greatest decrease of potential; mathematically E = -∇V. In one dimension Eₓ = -dV/dx, the minus sign shows a positive test charge feels force toward lower V. Forgetting the minus flips the field direction.

Memory trick: E = -gradient V → field downhill.

No isolated magnetic poles

“Snipping a bar magnet is like cutting a chocolate bar; each piece still has a north and a south side, never a lone pole.”

Gauss’s law for magnetism states ∮ B·dA = 0, meaning net magnetic flux through any closed surface is zero. Cutting a bar magnet therefore creates two smaller dipoles, each with its own north and south ends; no isolated monopole appears. The trap is to assume a cut piece can be a single pole, which never satisfies the law.

Memory trick: Cut → two dipoles, never a single pole.

Bohr's quantised orbits

“A skateboarder glides on a smooth rail without squeaking; only when he jumps off does a sound (photon) appear.”

Bohr postulated that electrons occupy only orbits with angular momentum L = nħ (n = 1,2,…). In these stationary states they do not emit radiation; light is emitted or absorbed only when the electron jumps between two levels, with hν = ΔE. Trap: assuming continuous radiation while in an allowed orbit.

Memory trick: Orbit silent, jump noisy.

Mass defect and binding energy

“When two magnets snap together, the combined weight is a hair lighter than the two separate pieces.”

Mass defect Δm = Σ m_nucleons – m_nucleus; it is always positive and gives binding energy B = Δm c². Use atomic masses and subtract the electron masses of the neutral atoms; ignoring electrons makes Δm too small.

Memory trick: Δm = Σ nucleon masses – nuclear mass.

Accuracy, precision and uncertainty

“A dart board’s bullseye shows accuracy; a tight cluster of darts shows precision.”

Accuracy measures closeness to the accepted value, precision measures repeatability. Random errors shrink with more trials, reducing uncertainty, but systematic calibration errors remain unchanged. The exam trap: calling a precise but biased set accurate.

Memory trick: Bullseye = accurate; cluster = precise.

Acceleration

“A car entering a roundabout feels a sideways push; that centripetal acceleration changes the direction of its velocity without altering its speed.”

Acceleration a = dv/dt is the vector rate of change of velocity. Its tangential component changes speed, while the normal (centripetal) component changes direction without affecting speed. A classic trap: at the top of a thrown ball v=0 but a= –g ≠0, so non-zero acceleration despite zero speed.

Memory trick: a = dv/dt; tangential → speed, normal → direction

Work–energy theorem

“Pushing a child on a swing, the rope’s tension does no work because it stays perpendicular to the child’s motion.”

The net work done on a particle equals its change in kinetic energy (Wnet = ΔK). This is always true, but constraint forces give zero work only when their line of action is perpendicular to the actual displacement of the point where they act; otherwise they can do non-zero work (e.g., a moving pulley or friction treated as a constraint).

Memory trick: Constraint work = 0 only if force ⟂ displacement of its application point.

Archimedes' principle

“A massive steel ship rides on water because the water it displaces weighs more than the ship itself.”

Archimedes’ principle: buoyant force = weight of displaced fluid = ρ_fluid g V_disp, acting upward through the centre of buoyancy. Trap: using the object’s volume instead of the displaced volume when partially submerged.

Memory trick: Buoyancy = weight of fluid pushed aside.

Polarisation

“Polarising sunglasses block glare by allowing only vibrations in one plane, just as a picket fence lets cars pass in one direction.”

Light, being transverse, has electric field vectors perpendicular to propagation; a polariser transmits only the component along its axis, eliminating the orthogonal component. Longitudinal waves like sound lack such perpendicular oscillations, so they cannot be polarised. Trap: assuming any wave can be polarised.

Memory trick: Transverse → polarise; Longitudinal → no.

RMS value

“A toaster’s heating element gets 220 V rms, equivalent to a 311 V peak that flashes each half-cycle.”

RMS value of a sinusoid is the DC voltage that would produce the same heating: Vrms = Vpeak/√2. For 220 V rms, Vpeak ≈ 311 V. The trap is mixing rms with average or peak in power formulas.

Memory trick: Vrms = Vpeak/√2, Irms = Ipeak/√2.

Depletion region

“The junction’s empty zone is like a sand-filled moat around a castle, keeping charges apart.”

The depletion region is a zone devoid of free carriers where ionised donors (n-side) and acceptors (p-side) create an electric field that opposes carrier diffusion, establishing the built-in potential. Toppers note the width is larger on the lightly doped side, not equal on both sides.

Memory trick: Moat width ∝ 1/√(doping).

Combination of errors in a product

“Mixing two solutions, the final concentration’s uncertainty comes from each ingredient’s measurement error.”

For products or quotients, the fractional (relative) uncertainties add: (ΔQ/Q) = (ΔA/A)+(ΔB/B) for Q = A·B or A/B. This also applies when a measured value is raised to a power, since the exponent multiplies the relative error. Ignoring this leads to under-estimating error in derived quantities.

Memory trick: Add % errors for × or ÷

Energy loss in a perfectly inelastic collision

“When two cars crash and lock together, the sudden silence of the crumpled metal reflects the kinetic energy turned into deformation.”

After sticking, vf = (m₁v₁+m₂v₂)/(m₁+m₂). Energy lost ΔKE = ½ μ (v₁−v₂)² where μ = m₁m₂/(m₁+m₂) is the reduced mass. A frequent mistake is using total mass instead of μ, which miscalculates the loss.

Memory trick: ΔKE = ½·(m1m2/(m1+m2))·(Δv)².

Minimum friction for rolling on an incline

“A bowling ball rolls down a slanted lane; if the wood is too polished, it slides instead of rolling.”

For pure rolling the static friction must give the torque for angular acceleration: f_req = (I/(mR²))·mg sinθ / (1+I/(mR²)). The surface can supply at most μ_s mg cosθ, so μ_min = (I/(mR²))·tanθ / (1+I/(mR²)). A frequent mistake is to set μ_min = tanθ, ignoring the inertia factor.

Memory trick: μ_min = β·tanθ/(1+β), β = I/(mR²)

Gravitational potential inside a solid sphere

“Inside a uniformly dense planet, the pull you feel grows like the tension in a spring as you move outward, while the potential drops like a downward-opening parabola.”

Inside a uniform sphere, the field g(r)=GM r/R³ (linear in r) and the potential V(r)=-GM(3R²-r²)/(2R³), a downward parabola. Students often apply the exterior 1/r law inside, which is wrong because outer shells cancel.

Memory trick: g∝r, V∝-(3R²-r²)

Floating-body oscillation

“A lighthouse buoy bobbing up-down after a wave hit shows the same period as a floating cylinder in a tank.”

For a vertical cylinder of constant cross-section A, displaced volume V_disp=A·l (l= submerged length). Restoring buoyant force ≈ ρgA·y gives simple harmonic motion with ω=√(g/l), so T=2π√(l/g). The period is independent of fluid density and cylinder mass; it holds only for small amplitudes, vertical motion, and negligible damping. A common trap is inserting ρ in the formula, which cancels out.

Memory trick: T=2π√(l/g) – length, not density

Decibel scale of sound

“Turning a speaker up from whisper to rock-concert adds about 60 dB, a million-times more intensity.”

Sound intensity level β = 10 log10(I/I0) with I0 = 10⁻¹² W/m². Because intensity ∝ pressure², pressure level uses β = 20 log10(p/p0). Each 10 dB step means tenfold intensity; a 3 dB rise ≈ doubles it. The classic pitfall is applying the 10 log formula to pressure, halving the correct dB value.

beta = 10 log(I/I0)

Memory trick: Intensity → 10 log; Pressure → 20 log

Wien's displacement law

“A filament’s colour shifts from orange to blue as its temperature rises, just like a streetlamp brightening.”

Wien’s law λ_max T = 2.898×10⁻³ m·K gives the wavelength of peak spectral radiance per unit wavelength. The common pitfall is mixing the λ_max of wavelength-distribution with that of frequency-distribution, which differ by a factor of ~1.76.

lambda_max T = constant

Memory trick: λ_max·T constant; don’t mix ν-peak

Equipotential surfaces

“Walking along a hill’s contour line feels no height change; similarly, moving on an equipotential surface does no electric work.”

Equipotential surfaces have constant V, so the line integral ∮E·dl = 0, forcing E to be perpendicular to the surface. This holds only for electrostatic fields; a time-varying magnetic field can introduce a tangential component. Forgetting this leads to wrong conclusions in induction problems.

Memory trick: Equipotential = contour → E ⟂ surface

Drift velocity and mobility

“Electrons sprint through silicon like cars on a highway; their speed per volt is the mobility, always taken as a positive speed.”

Mobility μ = |v_d|/E is defined as a positive magnitude; conductivity σ = n |q| μ, where q is the carrier charge magnitude (e for electrons). Using a signed μ mixes signs and can give wrong σ; keep μ positive and handle charge sign separately.

Memory trick: μ = speed per field (positive); σ = n·|q|·μ