Mechanics

Module aims

This module covers Classical Mechanics: Statics, Kinematics and Dynamics. The module provides a basis for subsequent courses in structural mechanics and dynamics, and flight mechanics which are taught in later years. The subjects covered include Newtonian physics, gravitation, friction, variational mechanics, simple motion, particle dynamics, vibrations, energy and momentum methods and basic orbital mechanics.

Learning outcomes

On successfully completing this module, you should be able to:

1. demonstrate understanding of the SI system of units, symbols and dimensions.
2. demonstrate understanding of Newton’s Laws and the Law of Gravitation, describe the concept of a ‘free body diagram’ and apply them to simple mechanics problems.
3. formulate the fundamental principles of mechanics in terms of vector algebra and solve, using vectors, some problems in 3-D statics and 3-D particle motion in Cartesian, cylindrical and polar co-ordinates.
4. demonstrate understanding of the laws of dry Coulomb friction and their application to the solution of simple problems including examples where a degree of friction is essential for correct operation.
5. explain the terminology used to describe vibrating systems, and establish and solve the differential equation for a damped or undamped single degree of freedom system undergoing free or forced, small amplitude vibration.
6. discuss the use the energy or momentum method, as appropriate, to solve some problems involving translation and rotation of rigid bodies.
7. describe the trajectory of a particle about a fixed body exerting gravitational attraction using appropriate terminology as well as formulate and solve equations for this simple orbital motion.

Module syllabus

The contents of the three areas covered in this module are described below:                                                                  

1) Statics: 
- Vector basics: review of vectors, scalar and vector products in mechanics: force component, work done, moment of a force, velocity due to angular rotation.
- Moments of inertia: calculation of moments of inertia of simple geometries.
- 3D-Statics: free body diagram, equivalent force systems, translation of a force, the wrench.
- Friction: Coulomb friction and applications examples. 

2) Kinematics: 
- Variational Mechanics: definition of a conservative force, work done and potential energy.  Equilibrium and stability of equilibrium.
- Simple motion: motion in a straight line, graphical integration of acceleration/time record.  Cylindrical polar co-ordinates. Coriolis acceleration. 

3) Dynamics 
- Particle Dynamics: integration of Newton’s Equation for rectilinear motion where the force is a constant, a function of velocity or a function of position.
- Mechanical Vibrations of Simple Systems: free, damped and forced vibration.
- Energy Methods: conservation of energy, kinetic energy of a rigid body.
- Momentum Methods: conservation of momentum, impact, angular momentum.
- Orbital Mechanics: central force motion, areal velocity, trajectory equation, circular, elliptic and escape trajectories, eccentricity from launch conditions, conservation of energy.

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological. The content is presented via a combination of slides, whiteboard and visualiser.

Assessments

This module presents opportunities for both formative and summative assessment.  
You will be formatively assessed through progress tests and tutorial sessions. 
You will have additional opportunities to self-assess your learning via tutorial problem sheets. 
You will be summatively assessed by a written examination at the end of the module.  

Reading list