3.11 Engineering physics 3.11.1 Rotational dynamics 3.11.1.1 Concept of moment of inertia 3.11.1.2 Rotational kinetic energy for a point mass.   for an extended object.  Qualitative knowledge of the factors that affect the moment of inertia of a rotating object.  Expressions for moment of inertia will be given where necessary. Factors affecting the energy storage capacity of a flywheel. Use of flywheels in machines. Use of flywheels for smoothing torque and speed, and for storing energy in vehicles, and in machines used for production processes. 3.11.1.3 Rotational motion 3.11.1.4 Torque and angular acceleration Angular displacement, angular speed, angular velocity, angular acceleration:  Representation by graphical methods of uniform and non-uniform angular acceleration. Equations for uniform angular acceleration:   Students should be aware of the analogy between rotational and translational dynamics. 3.11.1.5 Angular momentum 3.11.1.6 Work and power Conservation of angular momentum. Angular impulse = change in angular momentum;   where T is constant.  Applications may include examples from sport. Eng Phys 2 Awareness that frictional torque has to be taken into account in rotating machinery. Eng Phys 2 3.11.2 Thermodynamics and engines 3.11.2.1 First law of thermodynamics 3.11.2.2 Non-flow processes where Q is energy transferred to the system by heating, Δ U is increase in internal energy and W is work done by the system. Applications of first law of thermodynamics. Eng Phys 3 Isothermal, adiabatic, constant pressure and constant volume changes.     Application of first law of thermodynamics to the above processes. Eng Phys 3 3.11.2.3 The p–V diagram 3.11.2.4 Engine cycles Representation of processes on p–V diagram. Estimation of work done in terms of area below the graph. Extension to cyclic processes: work done per cycle = area of loop Expressions for work done are not required except for the constant pressure case, Eng Phys 4 Understanding of a four-stroke petrol engine cycle and a diesel engine cycle, and of the corresponding indicator diagrams. Comparison with the theoretical diagrams for these cycles; use of indicator diagrams for predicting and measuring power and efficiency. input power = calorific value × fuel flow rate Indicated power = area of p−V loop × no. of cycles per second × no. of cylinders Output or brake power: friction power = indicated power – brake power  Engine efficiency; overall, thermal and mechanical efficiencies.   A knowledge of engine constructional details is not required. Questions may be set on other cycles, but they will be interpretative and all essential information will be given. Eng Phys 5 3.11.2.5 Second Law and engines 3.11.2.6 Reversed heat engines Impossibility of an engine working only by the First Law. Second Law of Thermodynamics expressed as the need for a heat engine to operate between a source and a sink.    Reasons for the lower efficiencies of practical engines. Maximising use of W and QH for example in combined heat and power schemes. Eng Phys 6 Basic principles and uses of heat pumps and refrigerators.  A knowledge of practical heat pumps or refrigerator cycles and devices is not required. Coefficients of performance: Eng Phys 6

 3.12 Turning points in physics 3.12.1 The discovery of the electron 3.12.1.1 Cathode rays 3.12.1.2 Thermionic emission of electrons Production of cathode rays in a discharge tube. Turning Points 1 The principle of thermionic emission. Work done on an electron accelerated through a pd V 3.12.1.3 Specific charge of the electron 3.12.1.4 Principle of Millikan’s determination of the electronic charge, e Determination of the specific charge of an electron by any one method.  Significance of Thomson’s determination of   Comparison with the specific charge of the hydrogen ion. Condition for holding a charged oil droplet, of charge Q, stationary between oppositely charged parallel plates.   Motion of a falling oil droplet with and without an electric field; terminal speed to determine the mass and the charge of the droplet. Stokes’ Law for the viscous force on an oil droplet used to calculate the droplet radius.  Significance of Millikan’s results.  Quantisation of electric charge. Turning Points 2 3.12.2 Wave-Particle duality 3.12.2.1 Newton’s corpuscular theory of light 3.12.2.2 Significance of Young’s double slits experiment Comparison with Huygens’ wave theory in general terms. The reasons why Newton’s theory was preferred. Turning Points 3 Explanation for fringes in general terms, no calculations are expected. Delayed acceptance of Huygens’ wave theory of light. Turning Points 3 3.12.2.3 Electromagnetic waves 3.12.2.4 The discovery of photoelectricity Nature of electromagnetic waves. Maxwell’s formula for the speed of electromagnetic waves in a vacuum where eo is the permeability of free space and m0 is the permittivity of free space. Students should appreciate that e0 relates to the electric field strength due to a charged object in free space and mo relates to the magnetic flux density due to a current-carrying wire in free space. Hertz’s discovery of radio waves including measurements of the speed of radio waves. Fizeau’s determination of the speed of light and its implications. (Electromagnetic Waves)  (Fizeau's experiment) The ultraviolet catastrophe and black-body radiation. Plank’s interpretation in terms of quanta. The failure of classical wave theory to explain observations on photoelectricity. Einstein’s explanation of photoelectricity and its significance in terms of the nature of electromagnetic radiation. Turning Points 4 3.12.2.5 Wave–particle duality 3.12.2.6 Electron microscopes de Broglie’s hypothesis:   Low-energy electron diffraction experiments; qualitative explanation of the effect of a change of electron speed on the diffraction pattern. Turning Points 4 Estimate of anode voltage needed to produce wavelengths of the order of the size of the atom. Principle of operation of the transmission electron microscope (TEM). Principle of operation of the scanning tunnelling microscope (STM). Turning Points 4 3.12.3 Special relativity 3.12.3.1 The Michelson-Morley experiment 3.12.3.2 Einstein’s theory of special relativity Principle of the Michelson-Morley interferometer. Outline of the experiment as a means of detecting absolute motion. Significance of the failure to detect absolute motion. The invariance of the speed of light. Turning Points 5 The concept of an inertial frame of reference. The two postulates of Einstein’s theory of special relativity: 1. physical laws have the same form in all inertial frames 2. the speed of light in free space is invariant. Turning Points 6 3.12.3.3 Time dilation 3.12.3.4 Length contraction Proper time and time dilation as a consequence of special relativity. Time dilation: Evidence for time dilation from muon decay. Length of an object having a speed v 3.12.3.5 Mass and energy Equivalence of mass and energy:  Graphs of variation of mass and kinetic energy with speed. Bertozzi’s experiment as direct evidence for the variation of kinetic energy with speed. Top