Learning Goal Breakdown

Unit 3: Gravity and Electromagnetism

Topic 1: Gravity and Motion

Vectors

• Use vector analysis to resolve a vector into two perpendicular components.
• Solve vector problems by resolving vectors into components, adding or subtracting the components, and recombining them to determine the resultant vector.

Projectile motion

• Recall that the horizontal and vertical components of a velocity vector are independent of each other.
• Apply vector analysis to determine horizontal and vertical components of projectile motion.
• Solve problems involving projectile motion.
• Mandatory practical: Conduct an experiment to determine the horizontal distance travelled by an object projected at various angles from the horizontal.

Solve problems involving projectile motion in the absence of drag effects using:

• v_y = u_y + at
• s_y = u_yt + ½at²
• v_y² = u_y² + 2as_y
• v_x = u_x
• s_x = u_xt

Inclined planes

• Solve problems involving force due to gravity (weight) and mass using the mathematical relationship between them.
• Define the term normal force.
• Describe and represent the forces acting on an object on an inclined plane through the use of free-body diagrams.
• Calculate the net force acting on an object on an inclined plane through vector analysis.
• Forces acting on an object on an inclined plane include force due to gravity (weight), the normal force, tension, frictional force, and applied force.

Circular motion

• Describe uniform circular motion in terms of a force acting on an object in a perpendicular direction to the velocity of the object.
• Define the concepts of average speed and period.
• Solve problems involving the average speed of objects undergoing uniform circular motion.
• Define the terms centripetal acceleration and centripetal force.
• Solve problems involving forces acting on objects in uniform circular motion.

Formulas:

• 𝑣 = 2𝜋r / 𝑇
• 𝑎 = 𝑣² / r
• 𝐹𝑛𝑒𝑡 = 𝑚𝑣² / r

Gravitational force and fields

• Recall Newton’s Law of Universal Gravitation.
• Solve problems involving the magnitude of the gravitational force between two masses.
• Define the term gravitational fields.
• Solve problems involving the gravitational field strength at a distance from an object.

Formulas:

• 𝐹 = 𝐺𝑚𝑀 / 𝑟²
• 𝑔 = 𝐹 / 𝑚 = 𝐺𝑀 / 𝑟²

Orbits

• Recall Kepler’s laws of planetary motion.
• Solve problems involving Kepler’s third law.
• Recall that Kepler’s third law can be derived from the relationship between Newton’s Law of Universal Gravitation and uniform circular motion.

Formulas:

• 𝑇² / 𝑟³ = 4𝜋² / 𝐺𝑀

Topic 2: Electromagnetism

Electrostatics

• Define Coulomb’s Law and recognise that it describes the force exerted by electrostatically charged objects on other electrostatically charged objects.
• Solve problems involving Coulomb’s Law.
• Define the terms electric fields, electric field strength, and electrical potential energy.
• Solve problems involving electric field strength.
• Solve problems involving the work done when an electric charge is moved in an electric field.

Formulas:

• 𝐹 = (1 / 4𝜋𝜀₀) × (𝑄𝑞 / 𝑟²)
• 1 / 4𝜋𝜀₀ = 9 × 10⁹ N·m²·C⁻²
• 𝐸 = 𝐹 / 𝑄 = (1 / 4𝜋𝜀₀) × (𝑞 / 𝑟²)
• 𝑉 = ∆𝑈 / 𝑞

Magnetic fields

• Define the term magnetic field.
• Recall how to represent magnetic field lines, including sketching magnetic field lines due to a moving electric charge, electric currents, and magnets.
• Recall that a moving electric charge generates a magnetic field.
• Determine the magnitude and direction of a magnetic field around electric current-carrying wires and inside solenoids.
• Solve problems involving the magnitude and direction of magnetic fields around a straight electric current-carrying wire and inside a solenoid.
• Recall that electric current-carrying conductors and moving electric charges experience a force when placed in a magnetic field.
• Solve problems involving the magnetic force on an electric current-carrying wire and moving charge in a magnetic field.
• Mandatory practicals:
  • Conduct an experiment to investigate the force acting on a conductor in a magnetic field.
  • Conduct an experiment to investigate the strength of a magnet at various distances.

Formulas:

• 𝐵 = (𝜇₀𝐼) / (2𝜋𝑟)
• 𝜇₀ = 4𝜋 × 10⁻⁷ T·A⁻¹·m
• 𝐵 = 𝜇₀𝑛𝐼
• 𝐹 = 𝐵𝐼𝐿sin𝜃
• 𝐹 = 𝑞𝑣𝐵sin𝜃

Electromagnetic induction

• Define the terms magnetic flux, magnetic flux density, electromagnetic induction, electromotive force (EMF), Faraday’s Law, and Lenz’s Law.
• Solve problems involving the magnetic flux in an electric current-carrying loop.
• Describe the process of inducing an EMF across a moving conductor in a magnetic field.
• Solve problems involving Faraday’s Law and Lenz’s Law.
• Explain how Lenz’s Law is consistent with the principle of conservation of energy.
• Explain how transformers work in terms of Faraday’s Law and electromagnetic induction.

Formulas:

• ∅ = 𝐵𝐴cos𝜃
• 𝑒𝑚𝑓 = −𝑛∆(𝐵𝐴⊥) / ∆𝑡
• 𝑒𝑚𝑓 = −𝑛∆∅ / ∆𝑡
• 𝐼ₚ𝑉ₚ = 𝐼ₛ𝑉ₛ
• 𝑉ₚ / 𝑉ₛ = 𝑛ₚ / 𝑛ₛ

Electromagnetic radiation

• Define and explain electromagnetic radiation in terms of electric fields and magnetic fields.

Unit 4: Revolutions in Modern Physics

Topic 1: Special Relativity

Special Relativity

• Describe an example of natural phenomena that cannot be explained by Newtonian physics, such as the presence of muons in the atmosphere.
• Define the terms frame of reference and inertial frame of reference.
• Recall the two postulates of special relativity.
• Recall that motion can only be measured relative to an observer.
• Explain the concept of simultaneity.
• Recall the consequences of the constant speed of light in a vacuum, e.g., time dilation and length contraction.
• Define the terms time dilation, proper time interval, relativistic time interval, length contraction, proper length, relativistic length, rest mass, and relativistic momentum.
• Describe the phenomena of time dilation and length contraction, including examples of experimental evidence of the phenomena.
• Solve problems involving time dilations, length contraction, and relativistic momentum.
• Recall the mass–energy equivalence relationship.
• Explain why no object can travel at the speed of light in a vacuum.
• Explain paradoxical scenarios such as the twins’ paradox, flashlights on a train, and the ladder in the barn paradox.

Formulas:

• t = t₀ / √(1 − 𝑣² / 𝑐²)
• 𝐿 = 𝐿₀ √(1 − 𝑣² / 𝑐²)
• 𝑝 = 𝑚₀𝑣 / √(1 − 𝑣² / 𝑐²)
• ∆𝐸 = ∆𝑚𝑐²

Topic 2: Quantum Theory

Quantum Theory

• Explain how Young’s double-slit experiment provides evidence for the wave model of light.
• Describe light as an electromagnetic wave produced by an oscillating electric charge that produces mutually perpendicular oscillating electric fields and magnetic fields.
• Explain the concept of black-body radiation.
• Identify that black-body radiation provides evidence that electromagnetic radiation is quantised into discrete values.
• Describe the concept of a photon.
• Solve problems involving the energy, frequency, and wavelength of a photon.
• Describe the photoelectric effect in terms of the photon.
• Define the terms threshold frequency, Planck’s constant, and work function.
• Solve problems involving the photoelectric effect.
• Recall that photons exhibit the characteristics of both waves and particles.
• Describe Rutherford’s model of the atom, including its limitations.
• Describe the Bohr model of the atom and how it addresses the limitations of Rutherford’s model.
• Explain how the Bohr model of the hydrogen atom integrates light quanta and atomic energy states to explain the specific wavelengths in the hydrogen line spectrum.
• Solve problems involving the line spectra of simple atoms using atomic energy states or atomic energy level diagrams.
• Describe wave–particle duality of light by identifying evidence that supports the wave characteristics of light and evidence that supports the particle characteristics of light.
• Mandatory Practical:
  • Conduct an experiment (or use a simulation) to investigate the photoelectric effect. Data such as the photoelectron energy or velocity, or electrical potential difference across the anode and cathode, can be compared with the wavelength or frequency of incident light. Calculation of work functions and Planck’s constant using the data would also be appropriate.

Formulas:

• 𝜆ₘₐₓ = 𝑏/𝑇
• 𝐸 = ℎ𝑓
• ℎ = 6.626 × 10⁻³⁴ J·s
• 𝐸ₖ = ℎ𝑓 − 𝑊
• 𝑓 = ℎ / 𝑝
• 𝑛𝜆 = 2𝜋𝑟
• 𝑚𝑣𝑟 = 𝑛ℎ / 2𝜋
• 1 / 𝜆 = 𝑅 (1 / 𝑛ₓ² − 1 / 𝑛ᵢ²)

Topic 3: The Standard Model

The Standard Model

• Define the concept of an elementary particle and antiparticle.
• Recall the six types of quarks.
• Define the terms baryon and meson.
• Recall the six types of leptons.
• Recall the four gauge bosons.
• Describe the strong nuclear, weak nuclear, and electromagnetic forces in terms of the gauge bosons.
• Contrast the fundamental forces experienced by quarks and leptons.

Particle Interactions

• Define the concept of lepton number and baryon number.
• Recall the conservation of lepton number and baryon number in particle interactions.
• Explain the following interactions of particles using Feynman diagrams:
  • Electron and electron.
  • Electron and positron.
  • A neutron decaying into a proton.
• Describe the significance of symmetry in particle interactions.