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.
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.
Explore displacement/time and velocity/time graphs with this mouse motion sensor.
Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging
Find out some of the mathematics behind neural networks.
Find the equation from which to calculate the resistance of an infinite network of resistances.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Follow in the steps of Newton and find the path that the earth follows around the sun.
How fast would you have to throw a ball upwards so that it would never land?
Can you work out the natural time scale for the universe?
Read all about electromagnetism in our interactive article.
A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?
Get some practice using big and small numbers in chemistry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
This is the technology section of stemNRICH - Core.
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?
A simplified account of special relativity and the twins paradox.
How high will a ball taking a million seconds to fall travel?
See how the motion of the simple pendulum is not-so-simple after all.
A look at a fluid mechanics technique called the Steady Flow Momentum 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'.
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.
Explore the Lorentz force law for charges moving in different ways.
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
Where will the spaceman go when he falls through these strange planetary systems?
Problems which make you think about the kinetic ideas underlying the ideal gas laws.
Find out why water is one of the most amazing compounds in the universe and why it is essential for life. - UNDER DEVELOPMENT
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
Things are roughened up and friction is now added to the approximate simple pendulum
Explore the power of aeroplanes, spaceships and horses.
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
Can you arrange a set of charged particles so that none of them start to move when released from rest?
Work out the numerical values for these physical quantities.
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
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
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Can you match up the entries from this table of units?
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?
Show that even a very powerful spaceship would eventually run out of overtaking power
When a mixture of gases burn, will the volume change?
Ever wondered what it would be like to vaporise a diamond? Find out inside...