Extension Physics
Extension Physics will be part of the Oxbridge programme and runs in parallel with Advanced
Level Physics. It is designed to build on the foundation of advanced level physics as it is taught,
exploring principles and concepts that would be taught in some first year university physics and
engineering courses. It is primarily meant for the gifted and talented, particularly those who will go
on to study physics, engineering or mathematics at university.
Vector Notation and Dynamics
After studying this section pupils should be able to…
Use vector notation (i, j and k) to describe physical quantities such as force, displacement,
velocity, and acceleration.
Perform multiplication of vector calculations using dot and cross products.
Use calculus to derive equations of motion for bodies whose acceleration is non-linear such as
those approaching terminal velocity
Solve work done problems using vector notation and dot products.
Solve balanced moments problems using vector notation and cross products.
Rotational Dynamics
After studying this section pupils should be able to…
Calculate torque using vector notation and cross products.
Perform calculations with angular displacement, angular velocity and angular acceleration.
Define moment of inertia.
Perform calculations with torque, moment of inertia and angular acceleration.
Derive the moment of inertia of a uniform rod from its centre and edge.
Derive the moment of inertia of a circular disc through the axis of symmetry which is
perpendicular to the plane of the disc.
Oscillations
After studying this section pupils should be able to…
Justify the use of ei as the standard oscillatory function for the mathematical treatment of
oscillating systems.
Find a solution to the equation of motion of an un-damped oscillator showing its natural
frequency (o) in terms of the mass (m) and spring constant (k).
Find a solution to the equation of motion of a forced un-damped oscillator showing its amplitude
and phase in terms of the natural frequency (o), the driving frequency (), the maximum
driving force (Fo) and the mass (m).
Find a solution to the equation of motion of a damped oscillator showing its frequency in terms
of the natural frequency (o), the mass (m) and the damping constant (b).
Show quantitatively how the damping constant determines whether a damped oscillator is under
damped, critically damped or over damped.
Find a solution to the equation of motion of a forced un-damped oscillator showing its amplitude
and phase in terms of the natural frequency (o), the driving frequency (), the maximum
driving force (Fo), the damping constant and the mass (m).
Find the frequency and describe the normal modes of a given coupled oscillator.
Waves and Electromagnetic Radiation
After studying this section pupils should be able to…
Recall the wave equation for a propagating wave.
Show by substitution into the wave equation that expressions of the form ei(tkx) describe a wave
of unity amplitude propagating along the negative/positive direction of the x-axis.
Derive the intensity of the interference pattern produced by a single slit, double slit, and double
slit with finite apertures.
Recall that electromagnetic radiation has a particulate nature known as photons, and that photons
have an energy and momentum according to E = h ( ) and p = h/ ( k) respectively.
Recall that particles have wave-like nature and show how the wave nature of particles with mass
can be described by Schrödinger’s Time Dependent Equation.
Derive Schrödinger’s Time Independent Equation from Schrödinger’s Time Dependent
Equation.
Derive the solutions of an infinite potential well using the TISE.
Show how the solutions of a finite potential barrier show the effect of quantum tunnelling.
Use energy and momentum operators to find the Eigen values of given Eigen functions.
Recall the solution to symmetric potential wells.
Nuclear Physics
After studying this section pupils should be able to…
Derive the equation that governs the exponential decay of a sample of nuclei.
Calculate the time taken for a sample to reach a given number of nuclei.