# Module Information

Module Identifier
MP14010
Module Title
CLASSICAL DYNAMICS
2012/2013
Co-ordinator
Semester
Semester 1
Co-Requisite
None
Pre-Requisite
A-level Mathematics
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 x 1-hour sessions of lectures/seminars

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   Written Examination  70%
Semester Assessment Two assignment sheets  30%
Supplementary Assessment 2 Hours   Written Examination  100%

### Learning Outcomes

On completion of this module, students should be able to:

1. Describe the basic principles of dynamics.
2. Solve numerical problems in translational motion, rotational motion and oscillations, and interpret the results in the physical context.
3. Model problems in dynamics using mathematical equations.

### Brief description

The module provides an introduction to the classical theory of dynamics. It comprises three main parts, following a brief recap of vector manipulation. The first part covers classical kinematics, Newton's Laws of Motion, momentum, forces, work and mechanical energy. The second part introduces rotational motion and illustrates the parallels with translational motion. The theory of oscillations is introduced in the third part, covering the classical harmonic oscillator, resonance, and coupled oscillators.

### Aims

The module develops the student's understanding of the principles and techniques of dynamics. Emphasis is placed on solving problems, and numerical examples are provided for the student to practice. The module is appropriate as a first-year core module in Physics and Mathematics honours degree schemes, and it prepares the student to use the topics in more advanced Part 2 modules.

### Content

VECTORS (recap)
Vector and scalar quantities. Position vector. Orthogonal unit vectors.
Manipulation of vectors: addition, resolving, scalar and vector products.

TRANSLATIONAL MOTION
1. Kinematics of a particle: constant acceleration, projectile motion.
2. Newton's Laws of Motion: momentum, weight, contact forces on solids, friction, circular motion and centripetal force, drag force.
3. Work and Energy: work done by force, kinetic energy, power, conservative force, potential energy (gravitational and spring), conservation of mechanical energy.
4. Conservation of momentum: centre-of-mass, collisions, coefficient of restitution.

ROTATIONAL MOTION
1. Rotation of solid bodies: moment of inertia, angular momentum, torque, angular acceleration.
2. Parallels between translational and rotational motion.

OSCILLATIONS
1. Simple Harmonic Motion: period, amplitude, velocity, acceleration, energy.
2. Simple Harmonic Motion in mechanical systems.
3. Damped and forced oscillations, resonance.
4. Coupled oscillations: normal modes.

### Module Skills

Skills Type Skills details
Application of Number Numerical problems in examples sheets in the examination paper develop skills in application of number.
Improving own Learning and Performance Examples sheets and an electronic homework package encourage self-directed learning and improved performance. Solutions are provided to examples sheets. Electronic homework is assessed via the online grade books.
Problem solving Problem solving skills are developed throughout this module and tested in assignments and in the written examination.
Research skills Directed reading and the electronic homework package allow the student to investigate the topics covered in the module.
Subject Specific Skills Dynamics is a core topic in Physics and Mathematics.