## Pre-requisite modules

- None

## Co-requisite modules

- None

## Prohibited combinations

Occurrence | Teaching cycle |
---|---|

A | Autumn Term 2021-22 to Summer Term 2021-22 |

Classical mechanics is one of the cornerstones of physics. It provides methods for calculating the position, velocity, acceleration and other properties of the motion of point particles and extended bodies as function of time, if the forces acting are known. Classical mechanics is an important subject in its own right but it also forms the basis of several other branches of physical science; indeed many of the ideas incorporated in quantum theory have their origin in classical mechanics. This module commences with the study of translational motion in systems containing one or few particles. It then deals with rotational motion. Some of the central concepts of physics – such as momentum, force, energy, work, angular momentum and key conservation laws will be introduced. This module also provides an introduction to the ideas and concepts of Einstein’s special theory of relativity and how it relates to the classical material.

The Professional Skills component of this module aims to develop the core competencies and knowledge required of any astrophysicist, including a general introduction to the subject, basic IT skills, report writing, use of information resources, experimental techniques, problem solving and computer programming. This will be achieved through a mix of activities, including laboratories, workshops, lectures, programming classes and small group teaching. The knowledge and skills learnt will be further developed in later years.

**Introductory Python Programming (term 2)**

This course introduces problem solving using computers, using Python as the programming language. The most difficult aspect of programming is designing a step-by- step recipe (algorithm) to solve a given problem. This kind of logical problem solving is a useful skill which is highly valued in research and in the commercial world, and which all physicists should learn through practice. Once an algorithm has been designed, it must be implemented in a programming language, which for this course is Python. Python is a modern language which is freely available for Windows, Linux/Unix and Mac OS with extensive documentation, tutorials and extensions available online. It is easy to learn but very powerful, and is increasingly being used commercially and in scientific research. Students will learn how to create programs in the Python language to solve physics problems and then visualise the results in 2D and 3D. The emphasis is on problem solving, and teaching skills which students can then apply to other areas of their study.

**Classical mechanics and relativity**

- Explain and discuss the central concepts of classical mechanics, including force, energy, work, momentum, moments of inertia, torque and angular momentum
- Define inertial and non-inertial frames of reference
- Derive the key results presented in lectures
- Apply these results to seen and unseen physical situations by using them to set up a mathematical model and to find quantitative solutions
- Discuss qualitatively the limitations of classical mechanics
- Discuss the concepts and ideas that led to the theory of special relativity
- State Einstein’s two postulates of Special Relativity
- State the Lorentz transformation and apply it to simple problems
- Solve simple problems concerning the way that time is dilated and length contracted when clocks and objects are seen in uniform motion relative to an observer
- Describe and apply the relativistic Doppler effect
- Solve elementary problems involving objects moving at relativistic velocities

**Professional skills: Introduction to Experimental Laboratory**

- Demonstrate good experimental practice, including accurate record keeping,
- The planning and execution of experiments,
- The identification, assessment and analysis of errors
- Write a scientific report using the accepted structure and style

**Professional skills: Statistics**

- Calculate probabilities
- Write down expressions for binomial, Poisson and normal distributions and understand their applicability
- Apply the properties of the normal distribution to experimental errors
- Understand the statistical meaning of standard error

**Professional skills: Python**

- Employ problem-solving strategies to develop algorithms
- Know the difference between declarations, expressions and control statements in programming
- Modify simple Python programs
- Use the Python module system to use external libraries
- Define functions in Python to structure code
- Evaluate mathematical expressions using built-in math functions
- Modify 3D visualisation code to display animations

In addition students will:

- Use commercial office software applications confidently for scientific presentation.
- Be able to use the library and retrieve information from the library using both paper and online resources.
- Engage in constructive personal development planning activities.
- Use computer software (such as Python and Origin) for numerical and graphing applications in physics.
- Demonstrate “physicist” skills in small group discussions, for example, order-of- magnitude estimations, dimensional analysis, etc.
- Be aware of ethical issues in physics and astrophysics.

**Syllabus: Classical Mechanics and Relativity**

__Classical mechanics__

- One-dimensional kinematics: displacement, instantaneous/average velocity and acceleration, motion under constant acceleration and free-fall.
- Two-dimensional kinematics: position-, velocity- and acceleration-vectors, resolving into components, projectile motion, relative velocity in one and two dimensions.
- Circular motion: angular frequency, centripetal acceleration and uniform circular motion.
- Forces and Newton’s Laws: fundamental forces and interactions, Newton’s laws of motion and their applications, free-body diagrams, reaction forces, static and kinetic friction, dynamics of circular motion.
- Work and energy: definition of work, sign of work, the work-energy theorem, work with a constant force, work with a variable force, power, conservative forces, work and potential energy, force and potential energy.
- Momentum and collisions: Momentum and impulse, conservation of momentum, elastic and inelastic collisions, centre of mass, rocket propulsion.
- Rotational kinematics: Angular velocity and acceleration, comparison withlinear motion, energy and rotation, moments of inertia, calculation of moments of inertia for simple systems, perpendicular and parallel axis theorems and their derivation.
- Rotational dynamics: Angular momentum, torque, relationship between torque and angular momentum & angular velocity and angular acceleration,conservation of angular momentum and its consequences, and dynamics of simple systems with rotational and translational motion.

**Syllabus: Relativity**

- Ideas and thoughts that lead to the special theory of relativity
- Inertial frames of reference
- Einsteins postulates of special relativity
- Spacetime
- Events; simultaneous events
- Time dilation; proper time
- Length contraction; proper length
- Lorentz transformation; examples and consequences
- Relativistic addition of velocities
- Relativistic Doppler shift for electromagnetic radiation
- Relativistic definitions of linear momentum and energy
- New units e.g. mass in terms of MeV/c2, linear momentum in terms of MeV/c
- Relativistic total energy and rest energy (E=mc2)
- Conservation laws for relativistic (total) energy and momentum

**Syllabus: Professional Skills**

__Induction Activities (weeks 1 and 2, term 1):__

Introduction to communication skills, study skills, career planning, personal development planning (3 hour lecture). Library: tour of the JB Morrell library (1 hour) and information retrieval exercises. A basic introduction to IT (web, e-mail, etc) and use of Office applications for scientific presentation (3 hours of computer sessions).

__Statistics (weeks 4-7, term 1):__

Five lectures on basic concepts in probability and statistics, with weekly coursework problems. Covers the notion of probability and binomial, Poisson, and normal probability distributions.

__Introduction to Experimental Laboratory__

(weeks 2-3, term 1): Three short workshops on experimental measurement techniques, plotting scientific data, and recording data and analysing errors.

(weeks 4-5, term 1): A core experiment to be presented in a formal report (see First Year Laboratory Handbook for full details).

Scientific report writing (week 6, term 1): An introduction to writing scientific reports (1- hour workshop).

Problem solving skills (fortnightly, term 1): Small group discussions with your supervisor, to help develop “thinking-like- a-physicist” skills such as order of magnitude estimations, dimensional analysis, applying differential equations, and curve sketching and interpretation (5 x 1-hour tutorials).

**Introductory Python Programming (term 2) Syllabus**

- Problem solving strategies and algorithm development
- Computer programming fundamentals and Python
- Looping with for..in and while loops
- Control using if, elif and else
- Getting input from the user, and printing results
- Debugging and testing methods
- Pythons module system and importing libraries
- Defining functions and using built-in mathematical functions
- Using Visual Python to produce animations of mechanics simulations

Task | Length | % of module mark |
---|---|---|

Essay/courseworkClassical Mechanics & Relativity Assignment 1 |
N/A | 16 |

Essay/courseworkClassical Mechanics & Relativity Assignment 2 |
N/A | 16 |

Essay/courseworkClassical Mechanics & Relativity Assignment 3 |
N/A | 18 |

Essay/courseworkInduction and laboratory activities |
N/A | 5 |

Essay/courseworkLaboratory reports |
N/A | 10 |

Essay/courseworkMarking of lab books |
N/A | 5 |

Essay/courseworkPython: assignments totalling |
N/A | 20 |

Essay/courseworkStatistics |
N/A | 5 |

Essay/courseworkYork Strengths assessment |
N/A | 5 |

None

Task | Length | % of module mark |
---|---|---|

Essay/courseworkClassical Mechanics & Relativity Assignment 1 |
N/A | 16 |

Essay/courseworkClassical Mechanics & Relativity Assignment 2 |
N/A | 16 |

Essay/courseworkClassical Mechanics & Relativity Assignment 3 |
N/A | 18 |

Essay/courseworkInduction and laboratory activities |
N/A | 5 |

Essay/courseworkLaboratory reports |
N/A | 10 |

Essay/courseworkMarking of lab books |
N/A | 5 |

Essay/courseworkPython: assignments totalling |
N/A | 20 |

Essay/courseworkStatistics |
N/A | 5 |

Essay/courseworkYork Strengths assessment |
N/A | 5 |

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.

**Reading List: Classical Mechanics and Relativity**

H D Young and R A Freedman: *University Physics with Modern Physics *****

*The Feynman Lectures on Physics: Volume 1* (Addison Wesley) **

K S Krane: *Modern Physics* ***

A.P. French:* Special Relativity* **

**Reading List: Professional Skills**

*Practical Physics* by G L Squires (Cambridge University Press) ***

*Python Programming: An Introduction to Computer Science* by John Zelle **