This collection of STEM resources is based on the physical world. Resources are listed in order of stage.
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Core scientific mathematics
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
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chemNRICH
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 of chemistry at A-level and university.
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physNRICH
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
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engNRICH
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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Emmy Noether
Find out about Emmy Noether, whose ideas linked physics and algebra, and whom Einstein described as a 'creative mathematical genius'.
problem
Pinhole camera
Age
11 to 14
Challenge level
Make your own pinhole camera for safe observation of the sun, and find out how it works.
article
Ancient astronomical terms
Some explanations of basic terms and some phenomena discovered by
ancient astronomers
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Stemnrich - technology
Age
11 to 16
Challenge level
This is the technology section of stemNRICH - Core.
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Big and small numbers in physics
Age
14 to 16
Challenge level
Work out the numerical values for these physical quantities.
problem
Constantly changing
Age
14 to 16
Challenge level
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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The power of dimensional analysis
An introduction to a useful tool to check the validity of an equation.
problem
Bigger or smaller?
Age
14 to 16
Challenge level
When you change the units, do the numbers get bigger or smaller?
problem
Perfect eclipse
Age
14 to 16
Challenge level
Use trigonometry to determine whether solar eclipses on earth can be perfect.
problem
Guessing the graph
Age
14 to 16
Challenge level
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
problem
Construct the solar system
Age
14 to 18
Challenge level
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
problem
The amazing properties of water
Age
14 to 18
Challenge level
Find out why water is one of the most amazing compounds in the universe and why it is essential for life. - UNDER DEVELOPMENT
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Big and small numbers in the physical world
Age
14 to 16
Challenge level
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
problem
Alternative record book
Age
14 to 18
Challenge level
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
problem
Big and small numbers in chemistry
Age
14 to 16
Challenge level
Get some practice using big and small numbers in chemistry.
problem
Electric kettle
Age
14 to 16
Challenge level
Explore the relationship between resistance and temperature
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Resistance
Age
16 to 18
Challenge level
Find the equation from which to calculate the resistance of an
infinite network of resistances.
problem
Whose line graph is it anyway?
Age
16 to 18
Challenge level
Which line graph, equations and physical processes go together?
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Pumping the power
Age
16 to 18
Challenge level
What is an AC voltage? How much power does an AC power source
supply?
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Big and small numbers in physics - group task
Age
16 to 18
Challenge level
Work in groups to try to create the best approximations to these
physical quantities.
problem
Mach attack
Age
16 to 18
Challenge level
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
problem
Earth orbit
Age
16 to 18
Challenge level
Follow in the steps of Newton and find the path that the earth
follows around the sun.
problem
Lennard Jones potential
Age
16 to 18
Challenge level
Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges
problem
Diamonds aren't forever
Age
16 to 18
Challenge level
Ever wondered what it would be like to vaporise a diamond? Find out
inside...
problem
Escape from Planet Earth
Age
16 to 18
Challenge level
How fast would you have to throw a ball upwards so that it would never land?
problem
Poiseuille's equation
Age
16 to 18
Challenge level
Look at the flow of fluids down circular pipes.
problem
Moving Stonehenge
Age
16 to 18
Challenge level
A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.
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Modelling assumptions in mechanics
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
problem
Universal time, mass, length
Age
16 to 18
Challenge level
Can you work out the natural time scale for the universe?
problem
Motorbike momentum
Age
16 to 18
Challenge level
A think about the physics of a motorbike riding upside down
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Cannon balls
Age
16 to 18
Challenge level
How high will a ball taking a million seconds to fall travel?
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Striking gold
Age
16 to 18
Challenge level
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.
problem
Ramping it up
Age
16 to 18
Challenge level
Look at the calculus behind the simple act of a car going over a
step.
problem
The ultra particle
Age
16 to 18
Challenge level
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
problem
Pack man
Age
16 to 18
Challenge level
A look at different crystal lattice structures, and how they relate
to structural properties
article
Maths in the undergraduate physical sciences
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 topics (e.g. complex numbers) and their applications.
problem
New units for old
Age
16 to 18
Challenge level
Can you match up the entries from this table of units?
problem
Cobalt decay
Age
16 to 18
Challenge level
Investigate the effects of the half-lifes of the isotopes of cobalt
on the mass of a mystery lump of the element.
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Battery modelling
Age
16 to 18
Challenge level
Find out how to model a battery mathematically
problem
The not-so-simple pendulum 1
Age
16 to 18
Challenge level
See how the motion of the simple pendulum is not-so-simple after all.
problem
Hold still please
Age
16 to 18
Challenge level
Can you arrange a set of charged particles so that none of them
start to move when released from rest?
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Powerfully fast
Age
16 to 18
Challenge level
Explore the power of aeroplanes, spaceships and horses.
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The Lorentz force law
Age
16 to 18
Challenge level
Explore the Lorentz force law for charges moving in different ways.
problem
Go spaceship go
Age
16 to 18
Challenge level
Show that even a very powerful spaceship would eventually run out
of overtaking power
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The real hydrogen atom
Age
16 to 18
Challenge level
Dip your toe into the world of quantum mechanics by looking at the
Schrodinger equation for hydrogen atoms
problem
Ideal gases
Age
16 to 18
Challenge level
Problems which make you think about the kinetic ideas underlying
the ideal gas laws.
problem
Ideal axes
Age
16 to 18
Challenge level
Explore how can changing the axes for a plot of an equation can
lead to different shaped graphs emerging
problem
Reaction types
Age
16 to 18
Challenge level
Explore the rates of growth of the sorts of simple polynomials
often used in mathematical modelling.
problem
Eudiometry
Age
16 to 18
Challenge level
When a mixture of gases burn, will the volume change?
problem
Drug stabiliser
Age
16 to 18
Challenge level
How does the half-life of a drug affect the build up of medication
in the body over time?
problem
Levels of Bohr
Age
16 to 18
Challenge level
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
problem
Lunar leaper
Age
16 to 18
Challenge level
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?
problem
The not-so-simple pendulum 2
Age
16 to 18
Challenge level
Things are roughened up and friction is now added to the approximate simple pendulum
problem
Sweeping satellite
Age
16 to 18
Challenge level
Derive an equation which describes satellite dynamics.
problem
Whoosh
Age
16 to 18
Challenge level
A ball whooshes down a slide and hits another ball which flies off
the slide horizontally as a projectile. How far does it go?
problem
Gravity paths
Age
16 to 18
Challenge level
Where will the spaceman go when he falls through these strange planetary systems?
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Keep your momentum going
Age
16 to 18
Challenge level
A look at a fluid mechanics technique called the Steady Flow
Momentum Equation.