PH2011 Physics 2A

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Module description

This module covers the subjects of mechanics, special relativity, oscillations, and thermal physics. It is suitable for those who have taken the specified first year modules in physics and mathematics, or have good Advanced Higher or A-Level passes or equivalent in physics and mathematics. It includes lectures on the dynamics of particles and rigid bodies, Einstein's special theory of relativity, free, forced and damped harmonic motion, and lectures on thermal physics including elementary thermodynamics and the notion of entropy.

Additional information from school

Aims & Objectives

To present a broad and mathematically founded introductory account of mechanics, thermal physics, oscillations and special relativity.

The ability to reason through scientific concepts, to relate different concepts to one another and to solve qualitative and quantitative problems in the areas covered in the courses with a toolkit of problem-solving techniques.

Laboratory skills, including the planning of experimental investigations, the use of modern test equipment, and the construction of electronic circuits. An appreciation of the value of learning of physics as a transformative experience in terms of motivated use (using physics beyond the course e.g. in everyday situations) and expansion of perception (seeing the world through the lens of physics).

The practical work of the module will develop a competence in using some of the standard equipment in physics laboratories, the analysis of experimental uncertainties and the presentation of experimental data in scientific reports.

The module will develop the ability to reason through scientific concepts and to solve quantitative problems in the areas of classical mechanics, thermal physics, oscillations in physics and special relativity with a toolkit of problem-solving techniques.

Learning Outcomes

By the end of the module, students should be able to:

• Identify a hierarchy of physical concepts and mathematical equations pertinent to mechanics, oscillations, special relativity and thermal physics, understanding which are the most fundamental and which follow from the fundamental laws.
• Solve elementary problems in mechanics, being confident in correctly identifying concepts that are applicable to each problem and to correctly visualise and analyse the problem in order to allow a solution to be formulated.
• Embed previously acquired knowledge correctly within the more general framework of mechanics presented in the course and to be aware of the limits of applicability and connectivity of that previous knowledge and its relation to newly acquired knowledge.
• Be confident in the use of vectors, their manipulation, their transformation to different coordinate systems, and to be clear about why vectors are necessary to properly understand some problems. To be clear about when the reduction of a vector problem to a scalar one is possible or advantageous.
• Represent oscillatory motion physically, mathematically and graphically and explain the connections between these representations.
• Derive equations of motion for oscillatory systems and solve the resulting equations of motion, distinguishing between general and specific solutions.
• State the postulates of special relativity, and use them to derive the formulas for length contraction and time dilation.
• Solve problems involving spacetime coordinates of events in different reference frames, kinematics and dynamics in special relativity; draw and interpret spacetime diagrams.
• Give multiple examples of experimental evidence that supports the theory of special relativity.
• State the zeroth, first and second laws of thermodynamics, explain their physical meaning and relate them to the thermodynamic identity.
• Use the Lorentz transformations to find the spacetime coordinates of events in different reference
• Draw and interpret spacetime diagrams.
• Derive and apply the relativistic velocity addition formula.
• Give multiple examples of experimental evidence that supports the theory of special relativity.
• State the zeroth, first and second laws of thermodynamics, explain their physical meaning and relate them to the thermodynamic identity.
• Solve problems involving thermal expansion, heat capacity and the transport of energy by heating in terms of the thermal properties of materials.
• Appreciate the differences between reversible and irreversible processes.
• State the ideal gas law and equipartition theorem, describe the essential assumptions and conclusions of the kinetic theory of ideal gases, and apply these to a variety of different thermodynamic problems.
• Distinguish between the concepts of heat and work and perform and explain basic calculations for these quantities for ideal gases under various conditions. Apply these to selected thermodynamic cycles, including the Carnot cycle.
• State the thermodynamic and statistical definitions of entropy, explain the link between them, and relate changes in entropy to the reversibility of a process.
• Describe and demonstrate appropriate data gathering procedures.
• Clearly record experimental data with an associated uncertainty, performing calculations on data with a correctly propagated uncertainty for single- or multi-variable problems as required.
• Critically analyse results against accepted literature values.
• Communicate observations through a structured laboratory notebook.

Synopsis

Mechanics: Dynamics of a single particle, Newton's laws of motion, inertial reference frames. Momentum, conservation of momentum in absence of external forces. Central force problems: velocity and acceleration of particles in plane polar coordinates. Work, energy and power. Conservative forces, relation between force and potential energy. Friction. Torque. Conservation of angular momentum. Gravitation: Newton's gravitational force law, potential energy for point source. Dynamics of a system of particles: Centre of mass. Internal and external forces. Translational equation of motion. Torque. Angular momentum and kinetic energy of a rotating system. Rotational equation of motion. Rigid bodies. Moments of inertia. Parallel and perpendicular axis theorems.

Oscillations in Physics: Mathematical description of oscillations. Circular motion and simple harmonic motion (SHM). Energy in SHM. Examples of SHM: spring-mass systems, pendulums, other oscillating systems. Damped oscillations. Types of damping, Q factor. Forced oscillations. Resonance. Examples of resonant systems. Coupled oscillations and normal modes.

Thermal Physics: Temperature, pressure and translational kinetic energy. The thermodynamic temperature scale. The notion of thermal equilibrium. Degrees of freedom. Reversible and irreversible processes. The zeroth law. Ideal gases. Mean Free Path and Maxwell Speed Distribution. Types of thermometer. Thermal expansion (linear, area and volume), interatomic forces and Lennard Jones Potential, crystal structure, elasticity. Equations of state. Work, heat and the First law of thermodynamics. Heat capacity and phonons. Heat transport, conduction, convection and radiation. Phase changes and latent heat. Adiabatic processes, free expansion of a gas. Entropy and the second law of thermodynamics. Direction of time. Heat engines, heat pumps, refrigerators, efficiency. Entropy from a statistical viewpoint.

Special Relativity: Inertial frames and Galilean relativity. The Galilean transformation equations. The postulate of special relativity. Clock synchronisation and the relativity of simultaneity. Length contraction, time dilation, and the Lorentz transformations. Proper time, invariants, and space-time diagrams. Transformation of velocity. Relativistic Doppler effect. Relativistic momentum and energy. Conservation principles and relativistic collisions.

Mathematics Revision: Trigonometry, dimensional analysis, complex vectors, functions, graphs, differentiation, integration, differential equations, Taylor series.

Laboratory Work:

Direct entry to second year students initially follow a focused laboratory skills development programme that includes: precision and accuracy, error propagation, data analysis and graphical representation, experimental technique and laboratory notebook keeping. All students explore aspects of physics in a practical manner, broaden competence in various forms of experimental and diagnostic instrumentation and will develop data handling and interpretation skills.

Additional information :

Please also read the additional information in the School's handbook for first and second level modules that is available via https://www.st-andrews.ac.uk/physics-astronomy/students/ug/timetables-handbooks/

Accreditation Matters

This module contains some material that is or may be part of the IOP “Core of Physics”.