Module MATH1627: Dynamics and Relativity I

Department: Mathematical Sciences

MATH1627: Dynamics and Relativity I

Prerequisites

• Normally grade A in A-Level Mathematics (or equivalent)

Corequisites

• One of:
• Calculus I (Maths Hons) (MATH1081) OR Calculus 1 (MATH1061)
• AND one of:
• Linear Algebra I (Maths Hons) (MATH1091) OR Linear Algebra 1 (MATH1071)

Excluded Combination of Modules

• Maths for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Foundation of Physics 1 (PHYS1122)

Aims

• Students will gain an understanding of elementary classical Newtonian dynamics, consolidating and extending previous experiences in mechanics.
• Students will explore the basics of Special Relativity, culminating in the ability to solve relativistic problems and understand the differences from non-relativistic mechanics.

Content

• 1D dynamics: equations of motion; use of energy and potentials; simple harmonic oscillators including damping, resonance, and small oscillations; collisions.
• 3D dynamics: Charged particles in constant electromagnetic fields; potential energy, simple pendula, projectile motion.
• Central forces: polar coordinates; angular momentum; orbits.
• Special relativity: Galilean and Lorentz boosts; Spacetime diagrams; Time dilation, length contraction and velocity addition; Lorentz group, four-momentum, mass-energy equivalence.

Learning Outcomes

• Upon completion of the course, students will be able to:
• Understand and apply Newton’s laws to solve fundamental problems in mechanics:
• o Model point motion in Cartesian and polar coordinate systems.
• o Solve Newton’s second law in 1, 2 and 3 dimensions for a single particle.
• o Recognise oscillatory systems and understand the form of their solutions.
• o Manipulate vector equations representing electromagnetic fields.
• o Determine whether or not a given force is conservative.
• o Understand what it means for a system to be stable or unstable in the context of potentials.
• o Express velocity, acceleration and angular momentum in 2D polar coordinates.
• o Use concepts of energy, potential and momentum to model basic dynamical phenomena, including:
• ▪ collisions between two particles,
• ▪ charged particles moving in an electric field,
• ▪ motion in a central force.
• Use the tools and concepts of special relativity to solve problems involving time dilation, length contraction, simultaneity, and other relativistic effects.

• Students will have basic mathematical skills in the following areas: Modelling and spatial awareness.

• The ability to precisely formulate and solve dynamical problems.
• Understanding of special relativity and space time diagrams.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures introduce the basic concepts.
• Tutorials provide active engagement and feedback to the learning process.
• Fortnightly formative assignments to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required for the summative assessments.
• Fortnightly summative assessments consolidate learning and assess understanding of material.
• The end-of-year written examination provides a rigorous assessment of the mastery of the learning outcomes by the student.
• Students are expected to develop their knowledge and skills with self-study.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Formative and summative assessments in alternate weeks.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University