# Gwybodaeth Modiwlau

Module Identifier
PM14010
Module Title
Classical Dynamics
2018/2019
Co-ordinator
Semester
Semester 1
Mutually Exclusive
Pre-Requisite
A Level Mathematics or equivalent
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Tutorial 6 x 1 Hour Tutorials
Lecture 22 x 1 Hour Lectures

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   Written Examination  70%
Semester Assessment Coursework Assignments  30%
Supplementary Exam 2 Hours   Written Examination  100%

### Learning Outcomes

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

1. State and demonstrate an understanding of fundamental principles in classical dynamics.
2. Recall theory relating to translational motion, rotational motion and oscillations.
3. Apply appropriate mathematical techniques to translational motion, rotational motion and oscillations.
4. Solve well-defined numerical problems relating to translational motion, rotational motion and oscillations, and interpret the results in the physical context.
5. Construct well-defined mathematical equations to express problems in classical dynamics and explain the application of the equations in the specified contexts.

### Aims

The module develops the student's understanding of the principles and techniques of dynamics. Emphasis is placed on solving problems. 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.

### 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.

### 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, forces (including weight, normal, frictional, tension, elastic, drag), circular motion.
3. Work, Energy and Power: work done by force, kinetic energy, conservative force, power, potential energy (gravitational and spring), conservation of mechanical energy.
4. Centre of mass: system of particles, system of uniform density.
5. Collisions: conservation of momentum, coefficient of restitution.

ROTATIONAL MOTION
1. Rotation of solid bodies: angular velocity, angular acceleration, moment of inertia, angular momentum, torque.
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 and 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. Additional examples are provided on Blackboard.
Problem solving Problem solving skills are developed throughout this module and tested in assignments and in the written examination.
Research skills Directed reading and Blackboard examples allow the student to investigate the topics covered in the module.
Subject Specific Skills Dynamics is a core topic in Physics and Mathematics.

### Notes

This module is at CQFW Level 4