Forces in Space

Calculus 3 · Axiom Academy

A push has a strength and a direction. Watch two of them team up into one, then take the controls — the idea that runs all of Calculus 3. Fire a thruster and a probe drifts; fire a second one at the same instant and it does not zig-zag between them — it slides off in a single new direction, as if one push had done the whole job. A force carries two facts at once: how hard it pushes and which way. Quantities like that are vectors , and the whole of Calculus 3 is built on how they combine. Watch a 4 N push to the east and a 3 N push to the north act on the probe together. Lay the second arrow's tail on the first arrow's tip, and the single green arrow from start to finish is the resultant — the one push that replaces both. Here it lands at N. The resultant is just the two pushes added tip-to-tail — one arrow that stands in for both. Set the strength and direction of each force with the sliders — or grab a force's arrowhead right on the plot and swing it. The green resultant follows every move, and its live strength |R| and heading update as you go. Try to make the two forces cancel. Point the two forces opposite each other at equal strength and the resultant shrinks to zero — the pushes cancel. Break one push into east and north

This is the written version of the interactive lesson above. See the full Calculus 3 course.