Foundations of physics 1
**Prerequisites**
A-Level Physics and A-Level Mathematics.
**Corequisites**
(Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) or (Linear Algebra I (MATH1071) and Calculus I (MATH1061)).
**Aims**
* This module is designed primarily for students studying Department of Physics or Natural Science degree programmes.
* It provides the minimum core physics required for progression to Level 2 physics modules and should be taken by all students intending to study physics beyond Level 1.
* It provides courses in classical aspects of wave phenomena and electromagnetism, and introduces basic concepts in Newtonian mechanics, quantum mechanics, special relativity and optical physics.
* The module provides students with practice in the informal discussion of scientific ideas within a small group.
* It also provides students with opportunitites to develop their study skills. Such skills include being able to understand the difference between University and A-level physics; understanding how to engage with the course material efficiently and developing problem-solving strategies.
* It provides students with practice at synthesising and proposing new problems based on their understanding of the knowledge base.
* It will enable students to analyse a physical system and to formulate a piece of computer code that substantially solves a problem or models the behaviour.
**Content**
The course will contain the following fundamental topics.
* Mechanics: Motion in a straight line. Motion in 2 or 3 dimensions. Newton's Laws. Work and Kinetic Energy. Potential Energy and Energy Conservation. Momentum, impulse, and collisions. Angular velocity and angular acceleration. Rotational kinetic energy, moment of inertia. Torque. Angular momentum. Combined linear and angular motion. Equilibrium, centre of mass. Gravitation: force and energy. Kepler’s laws. Periodic motion and harmonic oscillators.
* Waves and optics: Mechanical waves and the wave equation. Wave velocity and energy transport. Interference of waves and normal modes. Sounds waves and the Doppler effect. The nature and propagation of light. Refraction, polarization, Snell and Malus law. Geometrical optics and ray tracing. Lenses and mirrors. Interference of light. Young's slits. Diffraction.
* Electricity and magnetism: Coulomb's law. Electric fields due to point charges. Charge distributions. Electric flux and non-uniform electric fields Gauss' law. Work done by and against electrostatic forces. Electric potential and potential energy. Capacitance. Potential energy stored in charged capacitors. Magnetic field and magnetic forces. Magnetic forces on current. Sources of magnetism: the Biot Savart Law. Ampere's law. Magnetic materials. Electromagnetic induction. Inductance. Potential energy stored in inductors. EM waves. Maxwell's equations.
* Circuits: DC and AC Electrical currents. Electromotive Force. Electrical resistance. Electrical power. Kirchoff's rules. Resistors in series and parallel. RL, LC and LCR circuits.
* Special relativity: Invariance of Physical Laws. Relativity of Simultaneity. Relativity of time intervals. Relativity of length intervals. The Lorentz transformations. Relativistic momentum. Relativistic work and energy.
* Quantum mechanics: Photoelectric Effect. X-ray production. Electron Waves. Wave-particle duality. Probability and Uncertainty. Atomic spectra and the Bohr model of the Atom. Wavefunctions and the 1-dimensional Schrödinger equation. Wave packets, stationary states and time dependence. Interpretation of wavefunction. Particle in a one-dimensional box. Potential wells. Potential barriers and tunnelling. Harmonic oscillator.
* Oscillations: Simple harmonic motion. Damped harmonic motion. Driven harmonic motion. Resonance (width, Q-factor, phase). Applications in mechanics, LCR circuits, atomic transitions; nuclear reactions; elementary particle reactions. Collisions, conservation and fields: Centre of momentum frame; rocket motion; relativistic collisions; conservation in fluid flow (continuity, Bernoulli's equation). Continuity in electromagnetism. Gauss' law in electromagnetism and gravity. Conservative force fields.
* Collisions, conservation and fields: Centre of momentum frame; rocket motion; relativistic collisions; conservation in fluid flow (continuity, Bernoulli's equation). Continuity in electromagnetism. Gauss' law in electromagnetism and gravity. Conservative force fields.
**Learning Outcomes**
Subject-specific Knowledge:
* Students will be able to apply knowledge of the concepts and principles of the following foundational areas of physics to unfamiliar problems: Mechanics; Waves and optics; Circuits; Oscillations; Electromagnetism; Quantum mechanics; Special Relativity.
* Students will be able to formulate and solve equations of motion for particles to describe and predict their dynamics. Students will be able to apply conservation laws in applicable circumstances as an alternative method.
* Students will be able to describe and predict the behaviour of light using both (i) the ray picture of geometrical optics and (ii) simple physical optics.
* Students will be able to analyse a simple circuit driven by DC or AC using circuit theory.
* Students will be able to analyse physical systems in terms of charges and electromagnetic fields and predict the behaviour of charges and fields using the relevant concepts.
* Students will be able to describe the quantum-mechanical behaviour of particles in simple potentials. They will be able to predict departures from classical behaviour.
* Students will be able to apply the Lorentz transformations in simple situations and describe the behaviour of dynamic systems at relativistic energies. They will be able to predict departures from non-relativistic behaviour.
* Students will be able to outline areas of physics where harmonic oscillations govern the behaviour. They will be able to analyse and predict the behaviour of general oscillating systems including in unfamiliar contexts.
* Students will be able to identify and apply conservation laws in analysing and describing physical systems. This includes applications of conservation laws to collision problems and the concept of a conservative field.
Subject-specific Skills:
* Students will become adept at problem solving and be able to analyse a simple physical problem and formulate a mathematical description of it. In some cases students will be required to manipulate or solve the resulting set of equations in order to explain or predict the system's behaviour.
* Students will be able to sketch and graph the response of a physical system to a given set of initial and boundary conditions.
* Students will be able to recognise a key piece of fundamental physics (such as resonance or conservation of momentum) in a variety of contexts and apply a similar detailed analysis irrespective of an unfamiliar context.
Key Skills:
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
* Teaching will be lectures, supported by tutorials.
* The lectures will provide the means to give a concise, focused presentation of the subject matter of the module.
* The lecture material will be explicitly linked to the contents of a single recommended textbook for the module, thus making clear where students can begin their private study.
* When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.
* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times (the Department has a policy of encouraging such enquiries).
* Regular problem exercises will give students the chance to develop their theoretical understanding and problem-solving abilities.
These problem exercises will form the basis for discussions in tutorial groups of typically six students.
* The tutorials will also provide an informal environment for students to raise issues of interest or difficulty.
* Student performance will be summatively assessed through written examinations, an open-book examination and an online test, and formatively assessed through problem exercises, progress tests and a Collection examination.
* The written examinations, open-book examination and online test will provide the means for students to demonstrate their acquisition of subject knowledge and the development of their problem-solving skills.
* The problem exercises, progress tests and Collection examination will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.
More details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS1122
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Foundations of physics 1
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or HaDEA. Neither the European Union nor the granting authority can be held responsible for them. The statements made herein do not necessarily have the consent or agreement of the ASTRAIOS Consortium. These represent the opinion and findings of the author(s).
