The Trade Between Two Halves
Last timeThe Number That Does Not Move
Conserved energy is rarely one thing sitting still. It is two things changing in step, and a turning point is where one of them has all of it.
The pendulum's total from the last lesson had two terms in it, and that was not
an accident of how it was written.
- how fast it is moving, whatever that means for the system at hand: a speed, an angular speed, a rate of stretch
- how much there is of the thing being moved, which sets how much speed is worth
- the position part, a single number worked out from where everything is, with no reference to motion at all
The reason the split is clean is that the two terms line up with the two halves
of the rule. The rule for the speed is where the forces act, and the forces come
from the position part. The rule for the position is where the speed acts. One
term per line of the rule.
Watching the trade
Below is a weight on a spring, with the two parts of its total drawn
separately. There is also a knob for the stiffness of the spring, which is worth
turning: it changes the whole character of the motion while changing nothing
about the arrangement being described here.
The lesson stops here
6 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents