Mechanics

Mechanics is the study of motion, forces, energy, and momentum — the foundational physics that describes how objects move and interact. This section covers everything from measurement techniques to gravitational fields and material properties.

• SI base units — kilogram, metre, second, ampere, kelvin, mole
• Derived units — newton ($\text{kg}\,\text{m}\,\text{s}^{-2}$), joule ($\text{kg}\,\text{m}^2\,\text{s}^{-2}$), watt ($\text{kg}\,\text{m}^2\,\text{s}^{-3}$)
• Prefixes — nano ($10^{-9}$), micro ($10^{-6}$), milli ($10^{-3}$), kilo ($10^3$), mega ($10^6$), giga ($10^9$)
• Scalars and vectors — distinguishing quantities that have direction from those that do not; vector addition and resolution

• Equations of motion — $v = u + at$, $s = ut + \frac{1}{2}at^2$, $v^2 = u^2 + 2as$
• Free fall — acceleration due to gravity $g = 9.81\,\text{m/s}^2$; projectile motion; independence of horizontal and vertical components
• Motion graphs — displacement-time (gradient = velocity), velocity-time (gradient = acceleration, area = displacement)

• Newton”s laws of motion — inertia, $F = ma$, action-reaction pairs
• Weight and mass — $W = mg$; the distinction between gravitational field strength and acceleration
• Drag and terminal velocity — the balance of weight and drag; why objects reach a terminal speed
• Momentum — $p = mv$; conservation of momentum; impulse $I = \Delta p = F\Delta t$

• Work done — $W = Fs\cos\theta$; the joule
• Kinetic energy — $KE = \frac{1}{2}mv^2$
• Gravitational potential energy — $PE = mgh$ (near Earth’s surface)
• Conservation of energy — energy cannot be created or destroyed; only transformed
• Power — $P = \frac{W}{t} = Fv$; the watt
• Efficiency — $\eta = \frac{\text{useful output}}{\text{total input}} \times 100\%$

• Circular motion — centripetal acceleration $a = \frac{v^2}{r}$; centripetal force $F = \frac{mv^2}{r}$
• Simple harmonic motion — $a = -\omega^2 x$; period $T = 2\pi\sqrt{\frac{m}{k}}$ (mass-spring), $T = 2\pi\sqrt{\frac{l}{g}}$ (pendulum)
• Resonance — driving frequency equals natural frequency; amplitude increases dramatically

• Gravitational field strength — $g = \frac{GM}{r^2}$ (radial); $g \approx 9.81\,\text{N/kg}$ near surface
• Gravitational potential — $V_g = -\frac{GM}{r}$; escape velocity
• Orbits — satellite motion; geostationary orbit conditions

• Density — $\rho = \frac{m}{V}$
• Hooke’s law — $F = k\Delta x$; spring constant; limit of proportionality and elastic limit
• Stress, strain, and Young’s modulus — $\sigma = \frac{F}{A}$, $\varepsilon = \frac{\Delta L}{L}$, $E = \frac{\sigma}{\varepsilon}$
• Stress-strain curves — elastic region, yield point, plastic deformation, ultimate tensile strength, fracture
• Energy stored — $E = \frac{1}{2}F\Delta x = \frac{1}{2}k(\Delta x)^2$

1. Resolve all vectors. In every mechanics problem, choose your axes and resolve forces and velocities into components. Never skip this step.
2. Check dimensional consistency. Verify that your final answer has the correct units. If asked for energy, your answer must be in joules.
3. Practise projectile problems. Separate horizontal (constant velocity) and vertical (constant acceleration) components. They are independent.
4. Understand the difference between conservation of momentum (always true in a closed system) and conservation of kinetic energy (only in elastic collisions).
5. Draw stress-strain curves. Be able to label the elastic region, yield point, UTS, and fracture point, and distinguish between brittle, ductile, and polymeric materials.

Follow the sidebar order. Each page provides physical principles, derivations, worked examples, and exam-style problems. Start with quantities and kinematics before moving to dynamics and energy.

This section provides comprehensive A-Level Physics content for Mechanics, covering all specification points with detailed explanations, worked examples, and practice questions.

Each page in this section includes:

• Definitions: Clear, precise explanations of key concepts
• Worked Examples: Step-by-step solutions with annotations
• Practice Questions: Multiple-choice and structured questions with mark schemes
• Common Pitfalls: Errors to avoid and how to fix them
• Exam Tips: Strategies for maximising marks in this topic

1. Read the introductory page to understand the topic overview
2. Work through each sub-topic in order
3. Attempt the practice questions before checking solutions
4. Use the flashcards to revise key terminology
5. Complete the diagnostic test to identify remaining gaps

• Core definitions and principles
• Application to examination-style questions
• Links to related topics across the specification
• Assessment objective alignment (AO1, AO2, AO3)

• Active Recall: Test yourself regularly rather than re-reading notes
• Spaced Practice: Revisit this topic at increasing intervals
• Interleaving: Mix with other topics during revision sessions
• Elaboration: Explain concepts in your own words

Focus on command word interpretation and mark scheme analysis. Practice timing yourself on questions to build speed and accuracy. Review examiner reports for this topic to understand common student errors.

Physics reveals that nature follows mathematical laws at every scale. Matter is made of atoms, forces arise from field interactions, and energy is conserved in every transformation. The power of physics lies in its predictive ability - from calculating projectile trajectories to designing particle accelerators. Understanding these principles helps us technology, predict natural phenomena, and appreciate the universe’s underlying order.

• Mechanics
• Waves
• Electricity
• Fields