Which line graph, equations and physical processes go together?

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

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

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

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

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.

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?

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

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.

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?

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

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

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

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?

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.

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

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.

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

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?

This is the technology section of stemNRICH - Core.

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

Derive an equation which describes satellite dynamics.

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

Work out the numerical values for these physical quantities.

A think about the physics of a motorbike riding upside down

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. . . .

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. . . .

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