The AQA A-level Physics Data and Formulae booklet

 The AQA A-level Physics Data and Formulae booklet

Here is an enhanced version of the AQA  A-Level Physics Data Sheet with context provided for each section and formula to help students understand where and how they are applied.

AQA A-Level Physics Data Sheet 

Fundamental Constants

These constants are universal values used across various topics in physics.

• Speed of light ($c$): $3.00 \times 10^8 \, \text{m/s}$
  Used in wave equations, especially in electromagnetic wave problems.
• Gravitational constant ($G$): $6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$
  Crucial for gravitational force and field strength calculations.
• Planck constant ($h$): $6.63 \times 10^{-34} \, \text{J s}$
  Used in quantum physics to relate energy and frequency of photons.
• Elementary charge ($e$): $1.60 \times 10^{-19} \, \text{C}$
  Represents the charge of a single proton or electron, often used in particle physics.
• Mass of proton ($m_p$): $1.67\times 10^{-27}\text{kg}$
• Mass of neutron ($m_n$): $1.67 \times 10^{-27} \, \text{kg}$
  
• Mass of electron ($m_e$): $9.11 \times 10^{-31} \, \text{kg}$
  These masses are used in atomic physics and calculations involving particles.
• Avogadro constant ($N_A$): $6.02 \times 10^{23} \, \text{mol}^{-1}$
  Links the microscopic world (atoms, molecules) to macroscopic quantities.
• Boltzmann constant ($k$): $1.38 \times 10^{-23} \, \text{J/K}$
  Relates temperature to the kinetic energy of particles in thermal physics.

Mechanics

Mechanics is the study of motion and forces acting on objects.

• Equations of motion: Used for objects moving with constant acceleration.
  • $v = u + at$: Final velocity.
  • $s = ut + \frac{1}{2}at^2$: Displacement over time.
  • $v^2 = u^2 + 2as$: Relation between velocity, acceleration, and displacement.
• Kinetic energy ($E_k$): $\frac{1}{2}mv^2$
  Energy of a moving object.
• Potential energy ($E_p$): $mgh$
  Energy stored in an object due to height in a gravitational field.
• Force ($F$): $ma$
  Newton's second law, used to relate mass, acceleration, and force.
• Work done ($W$): $Fd \cos\theta$
  Work is the transfer of energy when a force is applied over a distance.
• Power ($P$): $\frac{W}{t} = Fv$
  Rate of doing work or energy transfer.

Waves

Waves describe the transfer of energy without the transfer of matter.

• Wave equation: $v = f\lambda$
  Relates wave speed, frequency, and wavelength.
• Intensity: $I = \frac{P}{4\pi r^2}$
  Describes energy transfer per unit area, often used in light or sound.
• Refractive index ($n$): $n = \frac{\sin i}{\sin r} = \frac{c}{v}$
  Used in refraction problems to compare wave speeds in different media.

Electricity

Electricity involves the study of charges, currents, and their effects.

• Ohm’s law: $V = IR$
  Relationship between voltage, current, and resistance in a circuit.
• Resistance ($R$): $R = \rho \frac{L}{A}$
  Resistance depends on material properties and geometry.
• Power ($P$): $P = VI = I^2R = \frac{V^2}{R}$
  Describes energy transfer in electrical systems.
• Capacitance ($C$): $C = \frac{Q}{V}$
  Measures a capacitor's ability to store charge per unit voltage.

Thermal Physics

Thermal physics explores energy transfer and particle behavior.

• Ideal gas law: $pV = nRT$
  Relates pressure, volume, and temperature for an ideal gas.
• Mean kinetic energy: $E_k = \frac{3}{2}kT$
  Average energy of gas particles due to their motion.

Fields

Fields describe the influence of forces over a distance.

• Gravitational force ($F$): $F = \frac{Gm_1m_2}{r^2}$
  Force between two masses due to gravity.
• Electric force ($F$): $F = \frac{kq_1q_2}{r^2}$
  Coulomb’s law for forces between charges.
• Magnetic force: $F = Bqv \sin\theta$
  Force on a moving charge in a magnetic field.

Atomic and Nuclear Physics

This area studies atoms, nuclei, and their interactions.

• Energy of a photon: $E = hf = \frac{hc}{\lambda}$
  Relates a photon's energy to its frequency or wavelength.
• Nuclear decay: $N = N_0 e^{-\lambda t}$
  Describes the number of undecayed nuclei over time.
• Half-life: $T_{1/2} = \frac{\ln 2}{\lambda}$
  Time for half the nuclei in a sample to decay.
• Mass-energy equivalence: $E = mc^2$
  Fundamental relationship between mass and energy.