Which line graph, equations and physical processes go together?

This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

Look at the calculus behind the simple act of a car going over a step.

An introduction to a useful tool to check the validity of an equation.

Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.

A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.

Explore the Lorentz force law for charges moving in different ways.

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

See how the motion of the simple pendulum is not-so-simple after all.

Can you work out the natural time scale for the universe?

How fast would you have to throw a ball upwards so that it would never land?

Get some practice using big and small numbers in chemistry.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

When you change the units, do the numbers get bigger or smaller?

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

Problems which make you think about the kinetic ideas underlying the ideal gas laws.

Work in groups to try to create the best approximations to these physical quantities.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Work out the numerical values for these physical quantities.

Which units would you choose best to fit these situations?

Explore the power of aeroplanes, spaceships and horses.

Ever wondered what it would be like to vaporise a diamond? Find out inside...

How does the half-life of a drug affect the build up of medication in the body over time?

How high will a ball taking a million seconds to fall travel?

Things are roughened up and friction is now added to the approximate simple pendulum

Where will the spaceman go when he falls through these strange planetary systems?

Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges

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 look at different crystal lattice structures, and how they relate to structural properties

Can you arrange a set of charged particles so that none of them start to move when released from rest?

A look at a fluid mechanics technique called the Steady Flow Momentum Equation.

What is an AC voltage? How much power does an AC power source supply?

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

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?

Can you match up the entries from this table of units?

Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

Derive an equation which describes satellite dynamics.

Find out why water is one of the most amazing compounds in the universe and why it is essential for life. - UNDER DEVELOPMENT

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. . . .

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. . . .

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

A think about the physics of a motorbike riding upside down

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.