Physics Simulations
Mechanics you can push around. Each of these integrates the real equations of motion frame by frame, so the animation and the readout come from the same maths — change the launch angle and the arc, the range and the flight time all move together.
Why watch it rather than calculate it
A projectile formula tells you the range. It does not tell you that the same range comes from two different angles, or that the flatter one gets there sooner — you find that by moving the slider and noticing the arc change shape while the number stays put. Every simulator here is built around one of those moments, where the relationship is obvious in motion and invisible in an equation.
Where the numbers come from
All four run a step-by-step integration rather than a closed-form shortcut, which is what lets them handle the cases textbooks skip: a pendulum released at 60° where the small-angle formula is already several percent out, or a falling object whose drag rises with the square of its speed. Each page states its assumptions, shows the formula, and lists the sources its constants come from.
For coursework and for teaching
Every simulator writes its full state into the URL, so a link carries the exact setup you were looking at — useful for a worked answer, a lesson plan or a forum reply. Nothing you type is sent anywhere; the whole thing runs in your browser and keeps running offline once the page has loaded.
Frequently asked questions
Are these accurate enough to check homework with?
For the models they state, yes — each page shows its formula and a worked example computed from the same code that drives the animation, so the figures on the page and the figures in the tool cannot disagree. What you should check is whether your coursework uses the same assumptions. A question that ignores air resistance will not match the free fall simulator with drag switched on.
Why does the pendulum period differ from the formula I was taught?
The familiar 2π√(L/g) is an approximation that assumes a small swing. It is accurate to within a percent below about 20°, but at 60° it under-reads by roughly seven percent and the gap widens from there. The simulator integrates the real equation and shows both figures side by side so you can see exactly where the approximation starts to cost you.
Do they work on a phone?
Yes. The canvas scales to the screen, the controls are sliders sized for a thumb, and no simulation needs a keyboard. On a narrow screen the panel drops below the stage rather than beside it.