Tool guides
One guide for every tool: what it is for, the idea behind it, how to use it, real uses and a worked example.
- 3D vectors explained: sum, dot product, cross product and skew lines
What adding vectors, the dot product and the cross product mean in pictures, and how to find the angle and shortest distance between two lines in space.
- Angular momentum: why a spinning skater speeds up
Understand conservation of angular momentum, moment of inertia and rotational energy with a skater who pulls her arms in, and a worked example.
- Banked curves: why roads tilt and how fast a car can safely turn
How the normal force and friction keep a car on a banked curve, the ideal no-friction speed, the safe speed range, and a full worked example.
- Bill calendar: plan bills and pay days so you never run short
Learn how a monthly bill calendar with a running balance shows money gaps early, with a worked example and common mistakes.
- Binding energy per nucleon explained, with a worked example
Why nuclei weigh less than their parts, how mass defect gives binding energy, and why fission and fusion both release energy. A clear guide to the binding energy lab.
- Energy on a track: kinetic, potential and heat, and the loop
How kinetic and potential energy swap on a rolling ball, why friction makes heat, and how high a ball must start to get round a loop, with worked numbers.
- Equations of motion: how v = u + at, s = ut + ½at² and v² = u² + 2as fit together
The three equations of motion for steady acceleration, what each symbol means, and how to see them on a velocity-time graph. Solve a problem from three known values, and find a car's stopping distance.
- From DNA to protein: how a gene is read, and what a mutation does
Transcription, the genetic code and translation in plain words, with a fresh worked example of silent, missense, nonsense and frameshift mutations.
- How temperature, pH and inhibitors change enzyme activity
A guide to enzyme rates: the spot test, rate = 1 ÷ time, temperature and pH curves, Vmax and Km, and competitive versus non-competitive inhibitors, with a worked example.
- How to get numbers out of a graph image (graph digitizing)
Turn a picture of a graph into x and y numbers: calibrate the axes, click or trace the points, and copy a table. Includes a worked example and common mistakes.
- How to plan a trip budget and a monthly budget, step by step
Work out what a trip or project costs and how much to save each month, then turn your pay and bills into one monthly budget that shows what you can save. A plain guide to the budget calculator.
- How to plan your week fast, and save it as an image or PDF
Type plans such as “Gym 7am tue” and the weekly planner reads the day and time for you. Switch between week and month, tick plans off, and download the result as a PNG or A4 PDF.
- How to work out a protein's mass, pI and extinction coefficient
What molecular weight, isoelectric point, net charge and the 280 nm extinction coefficient mean, and how to get them from a sequence in your browser.
- How to write chemical formulae with the criss-cross method
Learn what valency is, how to cross valencies over to write ionic formulae, and how to find formula unit mass, with a worked example.
- Kepler's laws of planetary motion, with a launch you can change
Why orbits are ellipses, why planets sweep equal areas, why T² = a³, and how g changes above and below the Earth, with a fresh worked example.
- Natural selection: how a trait spreads, with a moth simulator
See how birds, bark colour, population size and chance change the share of dark moths over 60 generations, and how to read p and q.
- Pairwise sequence alignment: how to line up two DNA or protein sequences
What global, semi-global and local alignment mean, how gap scores change the answer, and how to read the score, identity and dot plot.
- Photosynthesis and limiting factors: the pondweed bubble experiment
How light, carbon dioxide and temperature set the rate of photosynthesis, why only one factor limits it at a time, and how to run the pondweed experiment on screen.
- Probability trees: how to read one and find P(A | B)
How a two-stage probability tree works, how to multiply along its branches, and how Bayes' theorem reverses it: given a result, how likely is the cause?
- Restriction digests: from cut sites to fragments and a gel
How restriction enzymes cut DNA at short sites, how to count the pieces from one or more enzymes in a plasmid, and how to predict the gel bands.
- VSEPR shapes explained: count electron pairs to predict a molecule's 3D shape
How VSEPR theory turns a formula into a 3D shape: count the bonded atoms and lone pairs around the central atom, then read off the shape, the ideal bond angle and the hybridisation. Worked examples for ClF₃ and NH₄⁺.