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# Module Code - Title:

PH4171 - MECHANICS

2022/3

3

3

1

0

3

6

N

PH4131

# Rationale and Purpose of the Module:

The purpose of this module is to enhance students' understanding of key concepts and models associated with classical mechanics, vibrations and waves. The objectives are to develop the mechanics of single particles and of systems of particles including vibrations and waves and rigid bodies, and to introduce Lagrangian and Hamiltonian methods which also provide background for quantum mechanics.

# Syllabus:

Mechanical vibrations: simple harmonic and damped simple harmonic motion, quality factor, forced oscillations, coupled oscillations. Waves: transverse and longitudinal waves, phase and group velocity, energy transported by waves, reflection and transmission of waves. Review of the principles of mechanics: inertial frames, Newtons laws of motion. Central forces: gravitation and Keplers laws, orbits, scattering. Systems of particles: centre of mass, linear momentum, rocket propulsion, kinetic energy. Rigid bodies: rotation and moments of inertia, angular momentum and kinetic energy, torque, principal axes, Eulers equations, gyroscopic motion. Noninertial reference systems: angular velocity vector, inertial forces, dynamics of a particle in a rotating coordinate system. Lagrangian mechanics: Hamiltons principle, generalised coordinates, Lagranges equations for conservative systems, Hamiltons equations.

# Learning Outcomes:

## Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

- Solve problems involving simple, damped and forced harmonic motion. - Describe and analyse the motion of coupled oscillators. - Describe and analyse wave motion. - Review and apply Newtons laws of motion to problems including central forces. and orbits, rocket propulsion, systems of particles and rigid bodies. - Derive the dynamics of a particle in a rotating coordinate system. - Derive Lagranges equations from Hamiltons principle. - Apply Lagranges and Hamiltons equations in simple cases.

## Affective (Attitudes and Values)

Discuss the importance of classical mechanics in physics.

## Psychomotor (Physical Skills)

- Perform experiments requiring precise measurement. - Use mechanical and electronic apparatus for observation and measurement.

# How the Module will be Taught and what will be the Learning Experiences of the Students:

Students will learn via interactive lecture, laboratory, experiential tutorial and problem based private study.

# Prime Texts:

French, A. P. (1971) Vibrations and Waves , Chapman & Hall
Fowles, G. R., Cassiday, G. L. (2004) Analytical Mechanics , Thomson Brooks Cole

# Other Relevant Texts:

M. T. Laugier (2008) Mechanics , unpublished notes

Autumn - 09/10