Classical mechanics is one of the cornerstones of physics. It provides methods for calculating the position, velocity, acceleration and other properties of the motion of point particles and extended bodies as function of time, if the forces acting are known. Classical mechanics is an important subject in its own right but it also forms the basis of several other branches of physical science; indeed many of the ideas incorporated in quantum theory have their origin in classical mechanics. This module commences with the study of translational motion in systems containing one or fewparticles. It then deals with rotational motion. Some of the central concepts of physics – such as momentum, force, energy, work, angular momentum and key conservation laws will be introduced. This module then expands on this classical material to provide an introduction to the ideas and concepts of Einstein’s special theory of relativity.
Module learning outcomes
At the end of this module successful students will be able to:
Apply dimensional homogeneity and dimensional analysis to simple physical systems.
Explain and discuss the central concepts of classical mechanics, including force, energy, work, momentum, moments of inertia, torque and angular momentum
Define inertial and non-inertial frames of reference
Derive the key results presented in lectures
Apply these results to seen and unseen physical situations by using them to set up a mathematical model and to find quantitative solutions
Discuss qualitatively the limitations of classical mechanics
Discuss the concepts and ideas that led to the theory of special relativity
State Einstein’s two postulates of Special Relativity
State the Lorentz transformation and apply it to simple problems
Solve simple problems concerning the way that time is dilated and length contracted when clocks and objects are seen in uniform motion relative to an observer
Describe and apply the relativistic Doppler effect
Solve elementary problems involving objects moving at relativistic velocities
Dimensions: Dimensional homogeneity and dimensional analysis
One-dimensional kinematics: displacement, instantaneous/average velocity and acceleration, motion under constant acceleration and free-fall.
Two-dimensional kinematics: position-, velocity- and acceleration-vectors, resolving into components, projectile motion, relative velocity in one and two dimensions.
Circular motion: angular frequency, centripetal acceleration and uniform circular motion.
Forces and Newton’s Laws: fundamental forces and interactions, Newton’s laws of motion and their applications, free-body diagrams, reaction forces, static and kinetic friction, dynamics of circular motion.
Work and energy: definition of work, sign of work, the work-energy theorem, work with a constant force, work with a variable force, power, conservative forces, work and potential energy, force and potential energy.
Momentum and collisions: Momentum and impulse, conservation of momentum, elastic and inelastic collisions, centre of mass, rocket propulsion.
Rotational kinematics: Angular velocity and acceleration, comparison with linear motion, energy and rotation, moments of inertia, calculation of moments of inertia for simple systems,perpendicular and parallel axis theorems and their derivation.
Rotational dynamics: Angular momentum, torque, relationship between torque & angular momentum & angular velocity & angular acceleration, conservation of angular momentum and its consequences, dynamics of simple systems with rotational and translational motion, Coriolis and centrifugal forces.
Ideas and thoughts that lead to the special theory of relativity
Inertial frames of reference
Einsteins postulates of special relativity
Events; simultaneous events
Time dilation; proper time
Length contraction; proper length
Lorentz transformation; examples and consequences
Relativistic addition of velocities
Relativistic Doppler shift for electromagnetic radiation
Relativistic definitions of linear momentum and energy
New units e.g. mass in terms of MeV/c2, linear momentum in terms of MeV/c
Relativistic total energy and rest energy (E=mc2)
Conservation laws for relativistic (total) energy and momentum