BSc Physics with Theoretical Physics

Advanced Dynamics

Desirable/Complementary Content:

• Mathematics 2 PHYS10372 
• Vibrations & Waves PHYS10302

To enhance knowledge and understanding of classical mechanics and relativity.

On successful completion of PHYS10672, a student will be able to:

1. Apply Newton's theory of gravitation to problems of planetary motion and space travel.
2. Use inertial forces to explain motion from the viewpoint of rotating frames of reference.
3. Derive the general relation between the angular velocity and angular momentum of a rigid body, and use this to solve problems in rotational dynamics.
4. Solve problems in relativistic dynamics using the covariant formalism and energy-momentum four vectors.
 

1.Preliminaries (3 Lectures)
Newton’s laws of motion
Linear and angular momentum, force and torque
The two-body system
2.  Gravitation (6 Lectures)
Force fields and potentials
Newtonian gravity
Kepler’s motion in a central force field
Particle orbits as conic sections and Kepler's laws
3. Noninertial Frames of Reference (3 Lectures)
Motion in rotating frames
Centrifugal and coriolis forces
4.  Rigid-Body Motion (6 Lectures)
Angular velocity and angular momentum vectors
Moment-of-inertia tensor
Principal moments of inertia
Euler's equations
Free rotation and stability
Gyroscopes
5. Relativistic Dynamics (6 Lectures)
Principles of special relativity
The covariant formalism
Lorentz transformations and relativistic invariance
Relativistic momentum and energy
Applications to relativistic kinematics - Syllabus and literature will be provided.

Feedback will be provided via solutions to the problem sheets, which will be made available electronically on Teachweb and Blackboard. More detailed feedback will be provided in the exercise class which are integrated within the 24 lectures.

Barger, V. D. & Olsson, M. G. Classical Mechanics: a Modern Perspective, (McGraw-Hill)

Forshaw, J. & Smith, A. G. Dynamics and Relativity, (Wiley)

Marion, J. B. & Thornton, S. T. Classical Dynamics of Particles and Systems, (Academic)
 

Spiegel, M. R. Schaum’s Outline of Theoretical Mechanics, (McGraw-Hill Book Company).
 

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £40,300 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.