AQA A-Level Physics 3.6 Further mechanics and thermal physics: a complete overview of circular motion, SHM, gases and kinetic theory

What module 3.6 actually demands

Further mechanics and thermal physics extends the year-one mechanics into rotation, oscillation and the behaviour of gases at the molecular level. The examiners test precise definitions, confident equation handling, and the ability to apply ideas such as resonance and kinetic theory to unfamiliar situations. This guide walks through the six topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Circular motion

Motion in a circle at constant speed still involves acceleration because the velocity direction changes. The key relations are the angular speed $\omega = 2\pi f$, the link $v = \omega r$, the centripetal acceleration $a = \frac{v^2}{r} = \omega^2 r$ and the centripetal force $F = \frac{mv^2}{r} = m\omega^2 r$. The crucial idea is that the centripetal force is provided by a real force such as tension, friction or gravity, and is always directed towards the centre.

Simple harmonic motion

Simple harmonic motion is defined by the condition that acceleration is proportional to displacement and directed towards equilibrium, $a = -\omega^2 x$. You must use the solutions for displacement, velocity and acceleration, the time period of a mass-spring system $T = 2\pi\sqrt{\frac{m}{k}}$ and a simple pendulum $T = 2\pi\sqrt{\frac{l}{g}}$, and the continuous interchange between kinetic and potential energy. The period is independent of amplitude.

Forced vibrations and resonance

Real oscillators experience damping, which removes energy and reduces amplitude. Light, heavy and critical damping have different behaviours. When a system is driven by a periodic force, the amplitude is greatest at resonance, when the driving frequency matches the natural frequency. Increasing damping lowers and broadens the resonance peak. Examiners love resonance curves and examples such as bridges and tuning circuits.

Thermal energy transfer

Thermal physics covers internal energy as the sum of the random kinetic and potential energies of molecules, the difference between temperature and energy, specific heat capacity through $Q = mc\Delta\theta$, and specific latent heat through $Q = ml$ for melting and boiling. Calorimetry calculations and the interpretation of heating and cooling curves recur in every series.

Ideal gases and kinetic theory

The gas laws (Boyle, Charles and the pressure law) combine into the ideal gas equation $pV = nRT = NkT$. The molecular kinetic theory model derives $pV = \frac{1}{3}Nm\overline{c^2}$ from the random motion of molecules, defines the root mean square speed, and links the mean molecular kinetic energy to absolute temperature through $\frac{1}{2}m\overline{c^2} = \frac{3}{2}kT$. Remember the assumptions of an ideal gas and always work in kelvin.

How module 3.6 is examined

A typical AQA profile for this module:

• Definitions and explanations. Defining SHM, stating the assumptions of kinetic theory, and explaining resonance and damping with a sketched curve.
• Calculations. Centripetal force, SHM period and energy, specific heat and latent heat, the ideal gas equation, and root mean square speed.
• Applied and graphical questions. Interpreting displacement-time graphs, resonance curves, heating curves and gas law graphs.
• Extended answers. Linking the kinetic theory to temperature, or explaining how damping affects a driven system.

Check your knowledge

A mix of recall and calculation questions covering module 3.6. Attempt them under timed conditions, then check against the solutions.

1. A car of mass $1000 \text{ kg}$ rounds a bend of radius $25 \text{ m}$ at $10 \text{ m s}^{-1}$. Calculate the centripetal force. (2 marks)
2. State the defining condition for simple harmonic motion. (2 marks)
3. A mass-spring system has $m = 0.40 \text{ kg}$ and $k = 16 \text{ N m}^{-1}$. Find the period. (2 marks)
4. Explain what happens to the resonance peak as damping is increased. (2 marks)
5. Calculate the energy needed to raise the temperature of $2.0 \text{ kg}$ of water ($c = 4200 \text{ J kg}^{-1}\text{K}^{-1}$) by $30 \text{ K}$. (2 marks)
6. State two assumptions of the molecular kinetic theory model. (2 marks)
7. A gas of $0.50 \text{ mol}$ occupies $0.012 \text{ m}^3$ at $300 \text{ K}$. Find its pressure ($R = 8.31$). (2 marks)
8. Calculate the mean kinetic energy of a molecule at $400 \text{ K}$ ($k = 1.38 \times 10^{-23}$). (2 marks)