| CODE | PHY1200 | ||||||||||||||||
| TITLE | Introduction to Classical Mechanics and Waves | ||||||||||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||||||||||
| MQF LEVEL | 5 | ||||||||||||||||
| ECTS CREDITS | 8 | ||||||||||||||||
| DEPARTMENT | Physics | ||||||||||||||||
| DESCRIPTION | This study-unit will present the mechanics - kinematics and dynamics - of point-like particles and rigid bodies in the Newtonian formulation; the wave component of the study-unit is introduced by one of the archetypical model in physics: the harmonic oscillator, and developed into the mathematical formalism of undulatory phenomena, e.g., interference and diffraction, as well as applied to the field of acoustic. Tools from Calculus and Linear Algebra will be extensively used both for the derivation of theoretical results and for the solution of problems presented during the study-unit. This study-unit paves the way of the scientific enquiry and understanding of natural phenomena in that it contains the basic physical quantities our knowledge of nature is based upon. Study-unit Aims: This study-unit aims to familiarize the students with fundamental quantities in physics whose range of applicability extends largely beyond Classical Mechanics and Waves. The students will be able to describe the phenomena of the macroscopic world in a quantitative way by utilising the scientific approach, to connect the acquired knowledge to observed results, and apply the formalism of Newtonian dynamics to physical models relevant to scientific applications. The study-unit will endow the students with the necessary theoretical concepts, ranging from energy to interference, in order to address the contents of all of the following study-units of the Physics programme. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - understand the range of application of the kinematic equations to solve dynamical problems in three dimensional space; - use Newton’s equations to address general dynamical problems; - understand the concept of central forces; - derive Kepler’s laws from Newton’s equations; - fathom the role of energy in physical phenomena; - individuate kinetic and potential energy in physical phenomena and relate potential energy and conservative forces; - solve two-body 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; - understand the relation between the moment of inertia tensor and angular momentum; - explain the superposition principle for the solutions of a harmonic oscillator; - describe transient and steady behavior of the driven damped harmonic oscillator; - individuate the normal modes of coupled harmonic oscillators; - explain the connection between the dynamics of a harmonic oscillator and the dynamics of waves; - explain simple waves phenomena; - distinguish between longitudinal and transverse waves; - understand the concept of dispersion relation; - distinguish between phase and group velocity; - connect standing waves and resonance; - recognise sound as longitudinal waves and understand the basics of acoustics; - understand wave dynamics phenomena from the superposition principles, such as, interference and diffraction. 2. Skills By the end of the study-unit 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; - 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; - describe the propogation of waves in space and time; - describe the propogation of sound in material mediums; - use the phasor formalism to add up sinusoidal waves; - apply Fourier analysis to wave phenomena; - describe wave phenomena such as interference, beats, and diffraction. Main Text/s and any supplementary readings: Main - R. Halliday, Walker: Principles of Physics. Wiley, 2014. Additional reading - R Richard, P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics. Addison–Wesley, 1964. |
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| ADDITIONAL NOTES | Pre-Requisite qualifications: At least an intermediate in Physics and Pure Mathematics | ||||||||||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Tony John George Apollaro |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
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 study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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