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

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

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

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.

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

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

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?

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

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

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

Explore the power of aeroplanes, spaceships and horses.

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

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

Which line graph, equations and physical processes go together?

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?

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

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

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

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

Show that even a very powerful spaceship would eventually run out of overtaking power

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.

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?

Which units would you choose best to fit these situations?

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

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

This is the technology section of stemNRICH - Core.

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

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

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. . . .

Get some practice using big and small numbers in chemistry.

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. . . .

Work out the numerical values for these physical quantities.

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

A think about the physics of a motorbike riding upside down

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

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

Derive an equation which describes satellite dynamics.

Some explanations of basic terms and some phenomena discovered by ancient astronomers