sources:

• text: Halliday, Resnick, Walker - Fundamentals of Physics

This section covers key physical principles, from classical mechanics to modern physics. If Diagnostics feels solid, move on; if not, the worked examples below are the fastest way to repair it before the exam.

Physics diagnostics are designed to identify gaps in your understanding before you begin deeper study. By completing these diagnostic tests, you can pinpoint which areas need the most attention and allocate your study time effectively. Think of diagnostics as a map of your current knowledge, they show you where you are and where you need to go.

Prerequisites: Review the prerequisite topics before attempting this section.

• Diag Mechanics

Diagnostic tests serve a different purpose from typical exams or practice problems. Rather than assessing your final understanding, diagnostics are formative assessments that help you and your instructors identify specific areas of strength and weakness. The results guide your study plan and ensure you focus your efforts where they will have the greatest impact.

A diagnostic test typically covers a broad range of topics within a subject area, presenting questions of varying difficulty. You are not expected to answer every question correctly, the purpose is to reveal patterns in your knowledge. If you answer kinematics questions correctly but struggle with dynamics, you know to prioritise Newton’s laws and force analysis.

After completing a diagnostic test, analyse your results carefully:

1. Identify your weakest areas, These are the topics where you scored lowest or felt most uncertain. Prioritise these in your study plan.

2. Check for prerequisite gaps, Physics is cumulative. If you struggle with energy conservation, you may need to revisit work and kinetic energy first.

3. Note conceptual misunderstandings, It is not enough to identify topics you find difficult; you need to understand why you find them difficult. Is it a mathematical issue (you cannot solve the equations) or a conceptual issue (you do not understand the underlying principle)?

4. Track your progress, Retake the diagnostic periodically to measure improvement. Seeing your scores improve over time is motivating and confirms that your study strategies are working.

• Understand the core principles and definitions covered in this section
• Apply key concepts to solve problems and answer exam-style questions
• Connect this material to prerequisite topics and related sections
• Identify your own knowledge gaps and develop targeted study plans
• Build confidence in approaching unfamiliar physics problems

Begin with the topic summaries, then work through the practice problems to test your understanding. Use the cross-references to link related concepts across subjects where applicable.

Before the test:

• Review your notes briefly, do not cram, but refresh your memory on key formulas and concepts
• Ensure you have the necessary mathematical tools (algebra, trigonometry, basic calculus where applicable)
• Set aside uninterrupted time, diagnostics are most useful when completed under realistic conditions

During the test:

• Read each question carefully before attempting to solve it
• If a question seems unfamiliar, write down what you know and what you think might be relevant
• Do not spend too long on any single question, mark it and return to it later
• Show your working clearly, even if you are unsure of the final answer

After the test:

• Review every question, including those you answered correctly
• For incorrect answers, identify the source of the error (conceptual, mathematical, or careless)
• For questions you skipped, attempt them again with your notes open, this reveals whether the issue was recall or understanding
• Create a study plan based on your findings

Physics is built on a small number of fundamental principles from which a vast array of phenomena can be explained. The diagnostic tests in this section assess your understanding of these foundational ideas across several domains:

Classical mechanics describes the motion of objects under the action of forces. It is the foundation of physics and encompasses:

• Kinematics, Describing motion without reference to forces. Key quantities include displacement ($s$), velocity ($v$), acceleration ($a$), and time ($t$). The equations of motion for constant acceleration are:

  • $v = u + at$
  • $s = ut + \frac{1}{2}at^2$
  • $v^2 = u^2 + 2as$
  • $s = \frac{(u+v)}{2}t$

• Dynamics, Explaining motion through forces. Newton’s three laws of motion are the cornerstone:

  1. An object remains at rest or in uniform motion unless acted upon by a net external force
  2. $F = ma$ (the net force equals mass times acceleration)
  3. For every action, there is an equal and opposite reaction

• Energy and work, The work-energy theorem states that the net work done on an object equals its change in kinetic energy: $W_{net} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$. Conservation of energy: $E_{total} = KE + PE = \text{constant}$ (in the absence of non-conservative forces).

• Momentum, Momentum ($p = mv$) is conserved in isolated systems. In collisions: $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$. Elastic collisions conserve both momentum and kinetic energy; inelastic collisions conserve momentum but not kinetic energy.

Waves transfer energy without transferring matter. Key concepts include:

• Wave equation, $v = f\lambda$ (wave speed equals frequency times wavelength)
• Transverse vs longitudinal waves, In transverse waves (e.g. light), oscillations are perpendicular to the direction of travel. In longitudinal waves (e.g. sound), oscillations are parallel.
• Superposition principle, When two waves overlap, the resultant displacement is the algebraic sum of individual displacements
• Interference, Constructive interference occurs when waves are in phase; destructive interference occurs when waves are out of phase
• Diffraction, The spreading of waves around obstacles or through openings. Significant diffraction occurs when the obstacle or opening is comparable in size to the wavelength

Thermodynamics deals with heat, energy, and work:

• First law of energy, $\Delta U = Q - W$ (the change in internal energy equals heat added minus work done by the system)
• Ideal gas law, $pV = nRT$ (pressure times volume equals moles times gas constant times temperature)
• Entropy, The second law of thermodynamics states that the total entropy of an isolated system never decreases. Entropy is a measure of the number of microscopic configurations consistent with a macroscopic state.

Electricity and magnetism are two aspects of the same fundamental force:

• Coulomb’s law, $F = k\frac{q_1 q_2}{r^2}$ (the force between two point charges)
• Ohm’s law, $V = IR$ (voltage equals current times resistance)
• Kirchhoff’s laws, Current is conserved at junctions (KCL), and the sum of voltage drops around a loop equals the applied voltage (KVL)
• Magnetic force on a moving charge, $F = qvB\sin\theta$

Modern physics extends beyond classical mechanics into the behaviour of matter and energy at the smallest and fastest scales:

• Special relativity, Time dilation: $\Delta t = \gamma \Delta t_0$ where $\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$. Mass-energy equivalence: $E = mc^2$.
• Quantum mechanics, The photoelectric effect demonstrates that light behaves as discrete packets (photons) with energy $E = hf$. The de Broglie wavelength: $\lambda = \frac{h}{p}$.
• Nuclear physics, Radioactive decay follows exponential law: $N = N_0 e^{-\lambda t}$. Half-life: $t_{1/2} = \frac{\ln 2}{\lambda}$. Mass-energy equivalence in nuclear reactions: $\Delta E = \Delta m c^2$.

Question: A car accelerates uniformly from rest at $2.5 \text{ m/s}^2$ for $8 \text{ s}$. It then travels at constant velocity for $12 \text{ s}$ before decelerating uniformly to rest in $6 \text{ s}$. Calculate the total distance travelled.

Solution:

Phase 1: Acceleration

• Initial velocity $u = 0$, acceleration $a = 2.5 \text{ m/s}^2$, time $t = 8 \text{ s}$
• Final velocity: $v = u + at = 0 + (2.5)(8) = 20 \text{ m/s}$
• Distance: $s_1 = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}(2.5)(8)^2 = \frac{1}{2}(2.5)(64) = 80 \text{ m}$

Phase 2: Constant velocity

• Velocity $v = 20 \text{ m/s}$, time $t = 12 \text{ s}$
• Distance: $s_2 = vt = 20 \times 12 = 240 \text{ m}$

Phase 3: Deceleration

• Initial velocity $u = 20 \text{ m/s}$, final velocity $v = 0$, time $t = 6 \text{ s}$
• Distance: $s_3 = \frac{(u+v)}{2} \times t = \frac{(20+0)}{2} \times 6 = 60 \text{ m}$

Total distance: $s_{total} = s_1 + s_2 + s_3 = 80 + 240 + 60 = 380 \text{ m}$

Question: A block of mass $5 \text{ kg}$ is placed on a rough horizontal surface. A horizontal force of $20 \text{ N}$ is applied to the block, and it accelerates at $2 \text{ m/s}^2$. Calculate the coefficient of kinetic friction between the block and the surface. ($g = 9.8 \text{ m/s}^2$)

Solution:

From Newton’s second law: $F_{net} = ma$

The net force is the applied force minus the friction force: $F_{applied} - f_k = ma$

$f_k = F_{applied} - ma = 20 - (5)(2) = 20 - 10 = 10 \text{ N}$

The normal force on a horizontal surface equals the weight: $N = mg = (5)(9.8) = 49 \text{ N}$

The coefficient of kinetic friction: $\mu_k = \frac{f_k}{N} = \frac{10}{49} \approx 0.204$

• Skipping prerequisite material before attempting this section: If you struggle with algebra or trigonometry, you will find physics problems unnecessarily difficult. Ensure your mathematical foundations are solid before diving into physics.

• Not practising problems after reading the theory: Physics is learned by doing, not by reading. You must work through problems to develop problem-solving skills and deepen understanding. Reading a solution and thinking “I understand” is not the same as being able to solve the problem independently.

• Failing to connect concepts across different topics: Physics topics are deeply interconnected. Energy conservation links mechanics, thermodynamics, and electromagnetism. Waves appear in optics, sound, and quantum mechanics. Look for these connections.

• Ignoring units and dimensions: Always check that your answer has the correct units. Dimensional analysis is a powerful tool for verifying your work. If you calculate a velocity and get units of kg, something has gone wrong.

• Confusing vectors and scalars: Velocity is a vector (has direction); speed is a scalar. Force is a vector; energy is a scalar. Mixing them up leads to sign errors and incorrect components.

• Forgetting to convert units: Physics problems frequently require unit conversions (e.g. km/h to m/s, cm to m, g to kg). Failing to convert is one of the most common sources of error.

• Rounding too early: Keep intermediate values in your calculator and only round the final answer. Premature rounding introduces cumulative errors.

• Review all equations of motion and know when each is applicable
• Practise free-body diagrams, identify all forces acting on an object before writing equations
• Check your answers by considering limiting cases (e.g. what happens as $t \to 0$ or $t \to \infty$?)

• Draw diagrams for wave phenomena (reflection, refraction, diffraction, interference)
• Know the conditions for constructive and destructive interference
• Understand the relationship between wave speed, frequency, and wavelength

• Draw energy diagrams for thermodynamic processes
• Distinguish between isothermal, isobaric, isochoric, and adiabatic processes
• Apply the first law of thermodynamics consistently, paying attention to signs

• Draw circuit diagrams before analysing them
• Identify series and parallel combinations before calculating equivalent resistance
• Apply Kirchhoff’s laws systematically, label all currents and voltage drops

• Fundamentals of Physics by Halliday, Resnick, and Walker, The standard university physics textbook
• University Physics by Young and Freedman, Comprehensive coverage with excellent worked examples
• The Feynman Lectures on Physics by Richard Feynman, Deep conceptual insights from a master physicist
• Six Easy Pieces by Richard Feynman, Accessible introduction to fundamental physics concepts

• Core concepts and definitions
• Worked examples with step-by-step solutions
• Practice problems for self-assessment
• Cross-references to related topics