Applications of conservation laws — AQA A-Level Physics

Conservation laws are fundamental principles in physics stating that certain quantities remain constant in a closed system. In AQA A-Level, you focus on conservation of energy, linear momentum, and charge. These laws allow you to predict outcomes of interactions without knowing the details of the forces involved, making them powerful tools for solving problems in mechanics, particle physics, and electricity.

This topic is essential because it connects many areas of the specification, from collisions and explosions to nuclear decay and particle interactions. Exam questions often require you to apply these laws in unfamiliar contexts, so a deep understanding of when and how to use them is crucial. Mastering conservation laws will also support your understanding of more advanced topics like circular motion and simple harmonic motion.

• →Conservation of energy: Energy cannot be created or destroyed, only transferred between stores. In a closed system, total energy is constant. Useful in problems involving gravitational potential energy, kinetic energy, and work done against friction.
• →Conservation of linear momentum: In the absence of external resultant forces, total momentum of a system remains constant. Momentum is a vector; always assign a positive direction and use signs correctly.
• →Conservation of charge: In any isolated system, the total electric charge remains constant. This applies to particle interactions (e.g., beta decay) and electric circuits.
• →Elastic vs inelastic collisions: In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not; some is dissipated.
• →Explosions and recoil: Initially at rest, total momentum is zero. After explosion, momenta of fragments sum to zero, so they move in opposite directions with equal magnitudes of momentum.

• State that β⁻ decay converts a down quark into an up quark, changing a neutron into a proton.
• State that β⁺ decay converts an up quark into a down quark, changing a proton into a neutron.
• Identify the emitted particles: an electron and an antineutrino in β⁻ decay, a positron and a neutrino in β⁺ decay.
• Show that charge is conserved in the quark-level change, for example the down quark charge of −1⁄3 changes to an up quark charge of +2⁄3 with the electron carrying away −1.
• Show that baryon number is conserved because the number of quarks remains three in each nucleon.
• Show that lepton number is conserved, with the electron and antineutrino balancing lepton number in β⁻ decay and the positron and neutrino balancing it in β⁺ decay.
• Use the quark composition of nucleons, udd for a neutron and uud for a proton, to justify the change.
• Recognise that the change of quark character is a weak interaction, not a strong or electromagnetic one.
• Assign charge to each particle and show that the total charge before and after an interaction is equal.
• Assign baryon number 1 to baryons, −1 to antibaryons and 0 to mesons and leptons, then show that the total is unchanged.
• Assign lepton number 1 to leptons, −1 to antileptons and 0 to hadrons, then show that the total is unchanged within each lepton family.
• Assign strangeness 0 to non-strange particles, −1 to strange particles such as K⁻ and Λ, and +1 to particles such as K⁺ and K⁰, then compare totals.
• State that strangeness is conserved in strong and electromagnetic interactions but can change in weak interactions.
• Use conservation laws to decide whether a proposed interaction is allowed or forbidden.
• Identify the interaction type from the particles involved and the conservation behaviour, for example a change in strangeness indicates a weak interaction.
• Apply the laws to examples such as β decay, pion–nucleon scattering and strange-particle decays.
• State that total energy is conserved in an interaction, including rest energy and kinetic energy.
• State that total momentum is conserved in an interaction, treating momentum as a vector with direction.
• Set up a before-and-after equation for energy, converting rest mass to energy where necessary using E = mc².
• Set up a before-and-after vector equation for momentum, taking account of opposite directions with positive and negative signs.
• Apply the principles to examples such as collisions, decays and annihilation to determine unknown quantities.
• Recognise that in annihilation at rest the total momentum is zero, so product particles must have equal and opposite momenta.

• 💡Write the quark-level change as a balanced equation before describing the nucleon change.
• 💡Check charge, baryon number and lepton number line by line after writing each decay.
• 💡Use the words down quark and up quark rather than d and u alone when explaining the change.
• 💡Link each emitted lepton to the conservation law it satisfies.
• 💡Make a table of charge, baryon number, lepton number and strangeness for each particle before comparing totals.
• 💡State the interaction type first, then use it to decide whether strangeness must be conserved.
• 💡Check each conservation law separately rather than combining them in one step.
• 💡Use the quark composition of hadrons to check baryon number and strangeness when unsure.
• 💡Draw a simple before-and-after diagram with arrows to show directions, which helps you assign correct signs to momentum values.
• 💡Write the general conservation statements first, then substitute values, so your method is clear even if the final arithmetic is wrong.
• 💡Check that your final answer is physically sensible, for example that a photon momentum is not zero when the initial momentum was non-zero.
• 💡Always define a positive direction before calculating momentum. This simple step prevents sign errors and shows clear reasoning.
• 💡When asked to 'show that' a quantity is conserved, explicitly calculate the total before and after, and state that they are equal. Do not just assume conservation.
• 💡For energy problems, identify all energy transfers and state the principle of conservation of energy. Use equations like ΔE_p = ΔE_k + work done against friction.

• Saying that a whole quark is emitted from the nucleus; the correction is that the quark changes flavour and leptons are emitted.
• Writing the β⁻ change as u → d; the correction is d → u for β⁻ decay and u → d for β⁺ decay.
• Omitting the antineutrino or neutrino; the correction is to include it so that lepton number is conserved.
• Treating the electron as a quark-level particle with baryon number; the correction is that the electron has lepton number 1 and baryon number 0.
• Giving mesons a baryon number of 1; the correction is that mesons have baryon number 0.
• Treating strangeness as always conserved; the correction is that strangeness can change in weak interactions.
• Confusing lepton number with baryon number; the correction is to assign lepton number only to leptons and antileptons.
• Forgetting that antiparticles have opposite baryon number, lepton number and strangeness to their particles.
• Treating momentum as a scalar and ignoring direction, which gives incorrect results; the correction is to assign positive and negative signs to momenta according to direction.
• Forgetting to include rest energy in energy conservation, so mass changes appear to violate conservation; the correction is to include rest energy using E = mc² for each particle.
• Assuming kinetic energy is always conserved in every interaction; the correction is to recognise that kinetic energy may change while total energy remains conserved.
• Students often think kinetic energy is always conserved in collisions. Correction: Only in perfectly elastic collisions is kinetic energy conserved; in most real collisions, it is not.
• Students treat momentum as a scalar and ignore direction. Correction: Momentum is a vector; you must assign a positive direction and use negative signs for opposite velocities.
• Students assume that if an object is stationary, its momentum is zero, but forget that a system can have zero total momentum even if parts are moving (e.g., explosion). Correction: Total momentum of a system can be zero if internal motions cancel out.

1. 1Day 1-2: Review the definitions and equations for conservation of energy, momentum, and charge. Make a summary sheet with key formulas and units.
2. 2Day 3-4: Practice basic calculations for momentum conservation in collisions and explosions. Focus on setting up equations with correct signs.
3. 3Day 5-6: Work through energy conservation problems, including those involving friction and gravitational potential energy. Check your answers against mark schemes.
4. 4Day 7-8: Attempt exam-style questions on particle interactions and nuclear decay, applying conservation of charge and momentum.
5. 5Day 9-10: Complete a past paper under timed conditions, then review mistakes and revisit weak areas.

• 📋Calculation of final velocity in collisions: Use conservation of momentum. Remember to consider whether the collision is elastic or inelastic and whether kinetic energy is conserved.
• 📋Explosion/recoil problems: Total momentum before is zero. Set up equation with opposite momenta. Often asks for speed or kinetic energy of fragments.
• 📋Energy conservation in motion: e.g., roller coaster or pendulum. Use ΔE_p = ΔE_k + work done against resistive forces. May involve multiple stages.
• 📋Particle physics conservation: Check conservation of charge, baryon number, lepton number in interactions. Often multiple-choice or short answer.