Centre-of-mass velocity is unchanged by internal forces

“When a firecracker bursts mid-air, the fragments fly apart but the explosion’s centre keeps moving straight.”

Internal forces are equal and opposite, so total momentum (and thus COM velocity) stays constant if no external net force acts. Explosions change individual speeds but not COM motion; the trap is assuming the COM stops moving.

Memory trick: COM momentum conserved – internal forces cancel

Torque and angular momentum — common mistake

“Measuring torque about the axle while computing L about the rim is like timing a runner from the start line but measuring distance from the finish.”

Both τ and L must be taken about the same point or axis; otherwise τ = dL/dt does not hold because the reference changes the lever arm. Forgetting this causes wrong answers, especially in rigid-body rotation problems.

Memory trick: Same point, same axis

Total energy of an orbit — common mistake

“When a satellite climbs to geostationary orbit, its total energy becomes less negative, not more bound.”

Raising a satellite to a larger radius increases its total mechanical energy (E moves toward zero). Mistaking “higher orbit = more bound” leads to sign errors in energy calculations.

Memory trick: Higher r ⇒ E ↑ (toward zero).

Damped oscillations — common mistake

“Seeing a pendulum’s swing slow, students often claim its period stays exactly the same.”

For a lightly damped oscillator the period becomes T' = 2π/√(ω₀²−β²), which is larger than the undamped period T₀ = 2π/ω₀. The common mistake is treating T as unchanged despite damping.

Memory trick: Damped period T' = 2π/√(ω₀²−β²) > T₀.

Beats

“When two guitar strings tuned slightly apart vibrate together, you hear a throbbing sound that pulses at the difference of their pitches.”

Beats occur when two close frequencies interfere, producing amplitude modulation at f_beats=|f1-f2|. The ear resolves the slow envelope only if |f1-f2| is ≤~20 Hz; larger gaps give two distinct tones. Trap: using too large a Δf eliminates audible beats.

Memory trick: Beat = |Δf|, not sum

First law and sign convention — common mistake

“A balloon expanding against the air loses internal energy, similar to a spring releasing its stored energy.”

In the first law work must be calculated with external pressure: W = ∫P_ext dV. Using the gas’s internal pressure for irreversible expansion gives the wrong sign. Classic mistake: treating W as positive for compression without adjusting sign.

Memory trick: Use P_ext for W, not P_int

Conductor in equilibrium — common mistake

“Imagine painting a metal ball; the paint only coats the outer skin, never see it seep inside the metal.”

A static conductor does not allow charge to reside in its bulk; free electrons move until they reside on the outermost surface. The common error is to picture charge uniformly filling the volume. Remember: any excess charge appears on the outer surface; only a cavity with internal charge forces induced charge on its inner wall.

Memory trick: Charge lives on skin, not inside.

Wheatstone bridge

“Balancing a seesaw with two kids on each side mirrors a Wheatstone bridge: when it’s level, the galvanometer reads zero.”

In a Wheatstone bridge, when the ratio of the two resistances in one branch equals that in the other (R1/R2 = R3/R4), the galvanometer current is zero and the bridge is balanced. The trap is applying the ratio condition without first confirming zero galvanometer current, or mixing up opposite arms.

Memory trick: Zero galvo → R1/R2 = R3/R4.

Biot-Savart law

“Each tiny wire segment is like a paddle stirring water; its field points ⟂ to both the segment and the line to the observation point.”

Biot-Savart: dB = (μ0/4π) I dl×r̂ / r². The direction follows from the right-hand rule on dl and the line to the point, giving a field perpendicular to the plane of dl and r̂. Integrating vectorially yields the total field. Students often drop the cross-product and add scalar magnitudes, losing the correct direction.

Memory trick: dl×r̂ → right-hand rule

LC oscillations

“A child on a playground swing trades height for speed, just as energy swaps between a capacitor’s voltage and an inductor’s current.”

In an ideal LC, energy alternates between the capacitor (½CV²) and the inductor (½LI²) at angular frequency ω = 1/√(LC), giving f = 1/(2π√LC). No resistance means perpetual oscillation. Trap: believing the frequency depends on amplitude; it is constant for linear LC.

Memory trick: ω = 1/√LC – like mass-spring ω = √(k/m).

Coherence — common mistake

“Two bulbs of the same colour are like two clocks ticking at the same rate but never aligned.”

Two independent sources, even if monochromatic, have random relative phase, so they cannot produce a fixed interference pattern. Only a single source split into two paths guarantees coherence. The common error is assuming same wavelength ensures interference.

Memory trick: Same λ ≠ same phase → no interference

Transistor as an amplifier

“A transistor amplifies like a tiny lever: a feather-light push on the base swings a heavy arm at the collector.”

In the active region Ic≈βIb and the voltage gain depends on load resistance. Proper bias keeps VCE in the linear region. Trap: using Ic=βIb in saturation or cutoff leads to distortion and wrong current.

Memory trick: BJT: Base pushes, Collector lifts → β = lift factor

Bandwidth and information

“Streaming a 4K video needs a wider pipe than a 480p clip, just like a river needs more width for higher flow.”

Shannon’s theorem gives maximum data rate C = B·log₂(1+SNR). For a fixed SNR, increasing bandwidth B raises C, so wider channels carry more information. However, noise power grows with B, reducing SNR; neglecting this trade-off can lead to unrealistic capacity estimates.

Memory trick: More BW → more bits, but noise rises

Hooke's law and elastic limit

“A kitchen spring scale reads correctly until the spring is stretched past its elastic limit, after which it stays elongated.”

Hooke’s law σ = E·ε is valid only up to the proportional limit where the stress-strain graph is linear. The elastic limit is the maximum stress that still allows full recovery on unloading and can lie just beyond the proportional limit. Exams often conflate the two—verify which limit the question targets.

Memory trick: P before E: Proportional limit precedes Elastic limit

T = 2u sin(theta)/g

“A basketball shot from ground level lands back after T = 2u sinθ/g seconds.”

The time of flight T = 2u sinθ/g applies only when launch and landing heights are equal and air resistance is ignored. If heights differ, the quadratic height equation must be used. Students often misuse this formula for unequal levels, getting wrong T.

T = 2u sin(theta)/g

Memory trick: Same level? Use T=2u sinθ/g.

Delta L = alpha L_0 Delta T

“On a scorching day, railway tracks lengthen, causing the familiar “sun kink” in the rails.”

ΔL = α L₀ ΔT assumes α is constant over the temperature interval, which holds for small ΔT and isotropic materials. For large temperature ranges or composites, α varies and the linear formula gives errors. Remember to check the validity range before applying.

Delta L = alpha L₀ Delta T

Memory trick: Small ΔT, constant α → linear ΔL = αL₀ΔT.

P = (1/3)rho v_rms^2

“When air from a fan hits your hand, the pressure you feel comes from countless random molecular hits from all directions.”

For an ideal gas with isotropic random motion, pressure P = (1/3) ρ v_rms² follows from momentum transfer on walls. It fails for directed streams or non-ideal gases where the velocity distribution is not Maxwellian. Remember the isotropy condition.

P = (1/3)rho v_rms²

Memory trick: P = 1/3 ρ v²_rms for random isotropic speeds

V = (1/(4pi epsilon_0)) sum(q_i/r_i)

“Summing potentials from point charges is like adding the heights of individual hills you see from a mountain peak, each height = k q/r.”

The electric potential at a point due to discrete charges is V = (1/4πϵ₀) Σ q_i / r_i, taking infinity as zero reference. Remember to keep the sign of each q_i and use the distance from the charge to the point, not between charges.

V = (1/(4pi epsilon₀)) sum(q_i/r_i)

Memory trick: V = k Σ q/r – add each hill’s height.

U = -m dot B = -mB cos(theta)

“A bar magnet dropped between horseshoe poles settles with its north pole down, the orientation of lowest U.”

Potential energy of a dipole in a uniform field is U = –m·B = –mB cosθ; it is minimum when the dipole aligns with the field (θ = 0) and maximum when opposite (θ = 180°). The negative sign ensures the torque does work to lower U. Trap: omitting the minus sign predicts the wrong stable orientation.

U = -m dot B = -mB cos(theta)

Memory trick: U lowest when cosθ=1 (aligned).

r_n = a_0 n^2/Z

“Like planets, the orbital radius grows with the square of the orbit number, but a heavier nucleus pulls it closer.”

The radius of the nth Bohr orbit is r_n = a₀ n² / Z, where a₀ is the Bohr radius and Z the atomic number. It shows that larger n gives larger orbits, while higher nuclear charge shrinks them. The exam trap is forgetting the Z in the denominator for hydrogen-like ions.

r_n = a₀ n²/Z

Memory trick: r ∝ n²/Z.

Fission and fusion energy — common mistake

“A fission event is like a tightly packed LEGO tower that, when split, loses a few bricks; those missing bricks turn into the burst of energy.”

In fission or fusion the total rest mass of the products is smaller than that of the reactants; the mass defect Δm converts to kinetic energy via E=Δm c². The classic trap is the sign: Δm>0 (mass loss) means energy released, Δm<0 means energy must be supplied.

Memory trick: Δm = mass reactants − mass products; Δm>0 → energy out

Experimental control and repeated trials — common mistake

“Mixing apples and oranges in a fruit salad and then averaging their taste scores is nonsense, just as averaging trials run under different conditions misleads.”

A common mistake is to average results from trials that were not performed under the same controlled conditions. This masks systematic errors and gives a misleading mean. Always ensure all controls are identical before averaging; otherwise treat each set separately.

Memory trick: Don’t mix conditions when averaging.

s = ut + ½at²

“A metro train that accelerates uniformly, pauses, then reverses still obeys s = ut + ½at² for each constant-a interval.”

The equation s = ut + ½at² assumes acceleration a is constant in magnitude and sign. It stays valid even if the velocity changes direction, provided a does not vary. A frequent trap is to reject the formula when the object reverses; the true limitation is a non-constant acceleration.

s = ut + ½at²

Memory trick: Constant a (including sign) → use formula; variable a → cannot.

PE = ½kx²

“Clicking a ball-point pen compresses a tiny spring, storing ½ k x² joules that snap the tip forward.”

Elastic potential energy of a spring obeying Hooke’s law is PE = ½ k x², where x is displacement from equilibrium. The formula holds only within the elastic limit; beyond that the spring hardens and the relation fails. A trap is using it for large deformations or forgetting that x is measured from the relaxed length.

PE = ½kx²

Memory trick: Spring PE = ½ k x²