Study-Unit Description

Study-Unit Description


TITLE Introduction to Classical Mechanics and Waves

LEVEL 01 - Year 1 in Modular Undergraduate Course



DESCRIPTION This study-unit will first focus on the mechanics of point-like 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 point-like 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.

Study-unit Aims:

This study-unit 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 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;
- 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 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;
- 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 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 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:


- 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 Pre-Requisite qualifications: Physics (Intermediate)

STUDY-UNIT TYPE Lecture and Tutorial

Assessment Component/s Assessment Due Resit Availability Weighting
Assignment SEM2 Yes 20%
Oral Examination SEM2 No 30%
Online Examination (2 Hours) SEM2 Yes 50%

LECTURER/S Tony John George Apollaro
Andre Xuereb

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 2020/1. It may be subject to change in subsequent years.