Balearic PAU Physics common mistakes
Balearic PAU Physics · Understand the traps and how to avoid them.
When computing gravitational potential energy of a two-body or multi-body system, the student sums only the pairwise terms involving the body named in the question (or forgets one pair entirely), producing V = −GMm/r instead of the full sum over all distinct pairs.
Textbook formulas are usually written for a single pair, so students pattern-match 'potential energy of the system' to one term and do not systematically enumerate pairs. The negative sign and the choice of zero at infinity also get lost when rushing.
What to do instead
Before substituting numbers, list every unordered pair of masses and write one −Gm_i m_j / r_ij term for each. For three bodies there must be three terms; for four, six. Check the count against n(n−1)/2 and confirm every term is negative before evaluating.
Treating gravitational field strength g and gravitational potential V as interchangeable: using g = GM/r² to answer a potential question, or claiming potential is zero where the field is zero (e.g. at the midpoint between two equal masses they state both are zero, when only the field cancels).
Both quantities are derived from the same GM/r family of formulas and both are called 'gravitational', so under exam pressure the student grabs whichever formula is recalled first. The vector-versus-scalar distinction is understood in theory but not applied when reading the question.
What to do instead
Adopt a two-step routine: first decide whether the question asks for a vector (field, force - direction matters, can cancel) or a scalar (potential, energy - add algebraically, cannot cancel to zero unless terms are opposite in sign). Then write the matching formula. For superposition problems, explicitly state 'field cancels by symmetry, potential adds' as a sentence in the answer.
In electrostatic superposition problems, adding field magnitudes arithmetically (E = E1 + E2) even when the two field vectors are not collinear, or reporting a magnitude without the direction angle required by the question.
Students memorize E = kQ/r² as a scalar recipe and only later remember it is a vector. Vector addition with components is a skill from mathematics that is not automatically transferred to physics contexts, and the direction is often treated as optional decoration.
What to do instead
Always draw the point and the two field vectors, then resolve into x and y components before summing. Compute the resultant magnitude with Pythagoras and give its direction as an angle measured from a stated axis. If the question says 'field at point P', treat a missing direction as an incomplete answer and mark yourself down in practice.
Applying the right-hand rule inconsistently for magnetic forces and induced currents: using the force rule (F = qv×B) when the question asks for the direction of the induced current, or getting the sign of the induced current reversed because the flux change direction was misidentified.
There are several similar-looking right-hand and left-hand rules (force on a moving charge, force on a current-carrying wire, induced current via Lenz's law) and they are easy to conflate. The sign of the flux change is a separate reasoning step that students skip.
What to do instead
Use a fixed written protocol: (1) state the direction of B; (2) state whether flux is increasing or decreasing; (3) apply Lenz to get the direction of the induced B; (4) only then use the right-hand rule to get the current sense. Write each of the four steps as a short line in the answer so the examiner can follow and partial credit is preserved.
Using the angular frequency ω directly as the frequency f in wave equations, e.g. writing v = ω/k but then substituting ω = 2πf incorrectly, or computing period as T = 2π/ω but reporting it as T = 1/ω. Also confusing the phase of a wave at a point with its displacement.
The symbols ω, f, T and k appear together in the standard harmonic wave expression y = A sin(ωt − kx) and are memorized as a block without the factor 2π being attached to the right one. Unit checks are rarely performed under time pressure.
What to do instead
Write the master relations on the first line of any wave problem: ω = 2πf, k = 2π/λ, v = fλ = ω/k, T = 1/f = 2π/ω. Substitute symbols first and only insert numbers at the end, then check that ω has units of rad/s and f of Hz. For phase questions, compute the phase argument ωt − kx explicitly rather than reasoning loosely about 'ahead' and 'behind'.
In standing-wave and interference problems, mixing up nodes and antinodes, or applying the path-difference condition for constructive interference (Δr = nλ) to a case where a phase reversal on reflection adds an extra half-wavelength that is ignored.
The node/antinode formulas look symmetric (spacing λ/2 either way) so the labels get swapped. The reflection phase shift is a subtle boundary-condition fact that is easily forgotten because it is stated once in the textbook and rarely practised.
What to do instead
Anchor the definitions physically: displacement is zero at a node and maximum at an antinode, so if the question mentions 'zero amplitude' it is a node. For any interference setup, first ask 'is there a phase reversal at either boundary?' and add λ/2 to the path difference if so. Sketch the standing wave with labelled nodes and antinodes before answering.
Applying the thin-lens or mirror equation with wrong signs because the Cartesian sign convention was not set up before substitution, and treating a virtual image as if it had a positive image distance in every convention.
Different textbooks and the Balearic syllabus use a sign convention that must be stated explicitly, and students copy formulas without recording which direction is positive. Magnification sign is then reported without interpretation.
What to do instead
At the top of every optics problem write the convention you are using (e.g. real-is-positive, distances measured from the optical centre, positive in the direction of incident light). Then list known quantities with signs before touching the formula. Interpret the sign of the image distance in words ('virtual, same side as object') and check the magnification sign is consistent with that statement.
In relativity problems, substituting the lab-frame time or length into the proper-time or proper-length slot, or applying the time-dilation formula when the question actually requires length contraction (or vice versa).
The Lorentz factor γ appears in both formulas and the two expressions look almost identical. The physical criterion - proper time is measured by a clock at rest with respect to the events, proper length by an observer at rest with respect to the object - is understood but not applied as a decision step.
What to do instead
Before calculating, write one sentence identifying the rest frame of the clock or the rod. Then choose: the interval measured in the rest frame is the shortest time (proper) and the longest length (proper); the other frame gets γ multiplied (time) or divided (length). Compute γ once and reuse it, and sanity-check that the dilated time is larger and the contracted length smaller.
Mishandling the photoelectric effect by using the photon energy hf as the maximum kinetic energy of the emitted electron, or by claiming emission occurs for any intensity once the frequency is below threshold.
The energy-conservation equation K_max = hf − W is simple, but students collapse it to K = hf and drop the work function, and the intensity-versus-frequency independence is a counter-intuitive result that is memorized as a phrase rather than understood as a consequence of one-photon-one-electron absorption.
What to do instead
Always write the full equation K_max = hf − W = hc/λ − hc/λ₀ and check that K_max ≥ 0 before predicting emission. State the threshold condition f > f₀ explicitly. When asked about intensity, answer in terms of the number of photons (current) rather than the energy per electron, and say so in one sentence.
In radioactive decay and nuclear problems, computing the mass defect in atomic mass units but substituting it into E = mc² without converting to kilograms, or using the parent nucleus mass instead of the mass difference between parent and products.
The unified atomic mass unit and the kilogram are both used in the same chapter, and the conversion factor 1 u = 931.5 MeV/c² is often memorized as a number without its unit meaning. The mass defect is a difference, and students sometimes take the absolute mass of one nucleus.
What to do instead
Write the mass defect as Δm = m_reactants − m_products with every term in the same unit, then convert once: either Δm in kg times c² in J, or Δm in u times 931.5 to get MeV. Keep a unit line under every calculation and check that the final energy is positive (a negative result means the reaction is endothermic or the subtraction is reversed).