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

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

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

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

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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?

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

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

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

Explore the power of aeroplanes, spaceships and horses.

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

Which line graph, equations and physical processes go together?

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?

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

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

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

Which units would you choose best to fit these situations?

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

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?

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

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?

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

This is the technology section of stemNRICH - Core.

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

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.

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

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

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

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

A think about the physics of a motorbike riding upside down

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

Derive an equation which describes satellite dynamics.

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

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

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. . . .

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?