CODE  PHY1197  
TITLE  Introduction to Classical Mechanics and Waves  
LEVEL  01  Year 1 in Modular Undergraduate Course  
ECTS CREDITS  6  
DEPARTMENT  Physics  
DESCRIPTION  This studyunit will first focus on the mechanics of pointlike particles, deriving the kinematic equations in one, two, and three dimensions using different coordinate systems. Subsequently, the causes producing the motion are investigated, i.e., the dynamics of a particle in the Newtonian formalism. Then, the conservation laws that follow from Newton’s equations are presented (momentum, energy, and angular momentum conservation laws). Hence the Newton’s laws in systems composed of many particles are investigated and the physics of collision of pointlike particles will be studied, as well as the theory of gravitation and planetary motion. Rotations in two and three dimensions are investigated in detail, with a special emphasis on rigid bodies. The moments of inertia will be evaluated via the use of multiple integrals and the concept of principal axes is introduced by matrix diagonalisation. The motion of a harmonic oscillator, via the use of differential equations, will be addressed, including also damping and driving. Finally, wave mechanics will be introduced with focus on sound waves. In this framework the general solution of a linear wave equation will be decomposed in a sum of harmonic motions. Studyunit Aims: This studyunit aims to serve as an introduction to the methods of physics. It will lay a great emphasis on building physical intuition and problem solving skills. Classical mechanics offers an ideal playground to introduce general concepts such as energy, momentum, angular momentum and conservation thereof. The study of harmonic vibrations and sound waves aims to offer to the students a theoretical background that is transferable to a range of fields including electromagnetism, optics and quantum mechanics. Learning Outcomes: 1. Knowledge & Understanding By the end of the studyunit the student will be able to:  understand the range of application of the kinematic equations to solve dynamical problems in three dimensional space;  describe how a trajectory can be represented as a graph, and how the velocity is related to the slope of the trajectory;  use Newton’s equations to address general dynamical problems;  derive Kepler’s laws from Newton’s equations;  understand the concept of central forces;  connect the conservation of momentum and angular momentum to Newton’s third law;  solve twobody collision problems;  decompose the motion of a rigid body as the sum of its center of mass motion and a rotation about the center of mass;  explain the superposition principle for the solutions of a harmonic oscillator;  describe transient and steady behavior of the driven damped harmonic oscillator;  explain the connection between the dynamics of a harmonic oscillator and the dynamics of waves;  explain simple waves phenomena. 2. Skills By the end of the studyunit the student will be able to:  learn to draw graphs and sketches as an essential step towards problem solving;  use the derivation to relate trajectory to velocity, and velocity to acceleration;  use the integration to relate velocity to trajectory and acceleration to velocity;  use conservation of momentum and energy to solve simple collision problems;  use conservation of energy to calculate the dynamics of a body subject to a conservative force also in the presence of frictionless constraints;  learn how to read a potential curve in the presence of a given total mechanical energy value;  manipulate vectors including calculating cross products and gradients;  become familiar with change of frame of references and coordinates, in particular polar coordinates;  calculate the moment of inertia of a rigid body and its principal axis;  calculate the torque acting on a rigid body;  use integration to calculate the moment of inertia of particularly symmetric bodies, e.g. a cylinder;  calculate the center of mass and angular momentum of a rigid body;  solve problems involving rotations in two and three dimensions, including the motion of a gyroscope;  use complex numbers to solve simple linear differential equations, in particular, the equation of motion of a driven damped harmonic oscillator;  find the normal mode decomposition of simple linear systems like a vibrating string or a pair of coupled harmonic oscillators. Main Text/s and any supplementary readings: Main  Halliday, Resnick, Walker:Principles of Physics, Wiley. Additional reading  R Richard P. Feynman, Robert B. Leighton, and Matthew Sands, "The Feynman Lectures on Physics" (Addison–Wesley). 

ADDITIONAL NOTES  PreRequisite qualifications: Physics (Intermediate)  
STUDYUNIT TYPE  Lecture and Tutorial  
METHOD OF ASSESSMENT 


LECTURER/S  Tony John George Apollaro Andre Xuereb 

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The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to studyunits available during the academic year 2020/1. It may be subject to change in subsequent years. 