(Course description last updated for academic year 2022-23).
Prerequisites

Pre-requisites for IA Physics are that students have studied maths for public examination at A level or equivalent and physics or the mechanics modules of further maths.

For this course it is assumed that students have completed the IA Physics dynamics course in the Michaelmas term.

 

Learning Outcomes and Assessment

At the end of this course students should be able able to:

(Rotational Mechanics):

1. Combine concepts from the first term course in mechanics be able to solve problems for extended bodies that are in equilibrium or accelerating using

a) Newton's Laws of motion linearly and rotationally

b) Conservation of momentum and angular momentum

c) Conservation of energy linearly and rotationally

d) The equations describing angular and circular motion

2. To understand and calculate the constant precession of a gyroscope.

 

(Special Relativity):

Primary objectives:

1. Describe and explain the experimental evidence for special relativity.

2. Derive and use the Lorentz transformations to relate, for example, displacement, time, velocity, momentum and energy in frames moving relative to one another at relativistic speeds.

3. Apply the energy-momentum invariant and relativistic energy and momentum equations to solve problems of particle collisions.

Secondary objective:

4. Draw time-distance diagrams to describe and understand relativistic problems in different frames of reference (e.g. the Earth and rocket frames)

Synopsis

Rotational Mechanics: 

Turning moments: lever balance; turning moment as a vector; moment of a couple; conditions for static equilibrium.

Centre of mass: calculation for a solid body by integration.

Moment of inertia: calculation of moment of inertia; theorems of parallel and perpendicular axes.

Circular motion: angle, angular speed, angular acceleration; as vectors; rotating frames; centripetal force.

Angular momentum: concept and definition; angular impulse; conservation.

Rotational kinetic energy: simple collisions involving angular rotation.

Gyroscope: how it works; precession.

Special Relativity: 

Historical development: problems with classical ideas; the Aether; Michelson-Morley experiment.

Inertial frames: Galilean transformation.

Einstein’s postulates: statement; events, and intervals between them; consequences for time intervals and lengths;

Lorentz transformation of intervals: simultaneity; proper time; twin paradox; causality; world lines and space–time diagrams.

Velocities: addition; aberration of light; Doppler effect.

Relativistic mechanics: momentum and energy; definitions; what is conserved; energy–momentum invariant. Nuclear binding energies, fission and fusion.

References

     

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