Forces at right angles
Physics Narrative for 14-16
Adding forces at right angles
Forces just add as vectors, tip to tail. So if they don't happen to all be along one line, then it really doesn't matter. Just so long as you place the vectors to be added tip to tail, the resultant can always be found by going from the tail of the first to the tip of the last.
There's a case which is both simple and special: the vectors to be added are at right angles to each other. We expect you'll realise why it's special if you remember working with vectors on gridded paper – how far you move along the paper doesn't affect how far you move up the paper.
You can rotate the graph paper without changing the vector, just as you can use different co-ordinate systems to describe where one village is with respect to another (for example, Ordnance Survey grid, magnetic bearing and distance, or latitude and longitude) without affecting how you have to travel to get from one to the other. The values of the ordered set of numbers representing the vector can change without changing the vector: just so long as you only translate, and don't rotate.
Vectors are ordered sets of numbers
Put more formally, components at right angles don't interact. All vectors are ordered sets of numbers, and only numbers in identical positions within the vectors interact.
Since force (a vector) sets acceleration (also a vector), which in turn sets how velocity (again a vector) accumulates, this non-interaction leads to general patterns of considerable interest. These patterns are most prominent when the vector addition is iterated over several cycles, and we'll come back to these later in episode 02, when predicting motions.