See how the motion of the simple pendulum is not-so-simple after
Advanced problems in the mathematical sciences.
Which line graph, equations and physical processes go together?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work in groups to try to create the best approximations to these
Look at the calculus behind the simple act of a car going over a
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
Find out some of the mathematics behind neural networks.
Derive an equation which describes satellite dynamics.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
chemNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of chemistry, designed to help
develop the mathematics required to get the most from your study. . . .
A look at different crystal lattice structures, and how they relate
to structural properties
How fast would you have to throw a ball upwards so that it would
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Read all about electromagnetism in our interactive article.
A look at the fluid mechanics questions that are raised by the
Get some practice using big and small numbers in chemistry.
An introduction to a useful tool to check the validity of an equation.
Dip your toe into the world of quantum mechanics by looking at the
Schrodinger equation for hydrogen atoms
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
Things are roughened up and friction is now added to the
approximate simple pendulum
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Explore the power of aeroplanes, spaceships and horses.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
When you change the units, do the numbers get bigger or smaller?
Explore the rates of growth of the sorts of simple polynomials
often used in mathematical modelling.
Which units would you choose best to fit these situations?
How does the half-life of a drug affect the build up of medication
in the body over time?
Where will the spaceman go when he falls through these strange planetary systems?
How high will a ball taking a million seconds to fall travel?
Can you work out the natural time scale for the universe?
Investigate why the Lennard-Jones potential gives a good
approximate explanation for the behaviour of atoms at close ranges
Problems which make you think about the kinetic ideas underlying
the ideal gas laws.
Explore the Lorentz force law for charges moving in different ways.
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
Show that even a very powerful spaceship would eventually run out
of overtaking power
Can you match up the entries from this table of units?
What is an AC voltage? How much power does an AC power source
A look at a fluid mechanics technique called the Steady Flow
Follow in the steps of Newton and find the path that the earth
follows around the sun.
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
Investigate some of the issues raised by Geiger and Marsden's
famous scattering experiment in which they fired alpha particles at
a sheet of gold.
A ball whooshes down a slide and hits another ball which flies off
the slide horizontally as a projectile. How far does it go?
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
Explore how can changing the axes for a plot of an equation can
lead to different shaped graphs emerging
Can you arrange a set of charged particles so that none of them
start to move when released from rest?
An article about the kind of maths a first year undergraduate in
physics, engineering and other physical sciences courses might
encounter. The aim is to highlight the link between particular
maths. . . .
Find out how to model a battery mathematically