One Pattern, Two Domains: Why F=ma and V=IR Are the Same Equation
July 2026
Original clip: @21xooaes on X, 2026-07-29, reposting a video by Ali Alqaraghuli, PhD — the same NASA Postdoctoral Program fellow behind Five Equations, Told as One Story.
The move that makes this worth featuring
Alqaraghuli puts $F=ma$ and $V=IR$ side by side and argues both are conventionally written in a way that hides the one thing that actually matters: which quantity is the cause, and which is the effect. This isn’t a rehash of the F=ma material already covered in Five Equations — the real point here is the second equation most people never think to compare against it: Ohm’s Law.
$a=F/m$ and $I=V/R$: the same reframe, twice
Mechanics. $F=ma$ is what gets memorized and printed in every textbook. Rewritten as $a=F/m$, it reads as physics instead of algebra: a force is applied, and acceleration is what happens as a result, throttled by however much mass is in the way. He illustrates it with a ball on a ramp — a push (the cause) produces rolling (the effect), slowed by the ball’s own mass acting as inertial resistance to that push.
$$F=ma \quad\longrightarrow\quad a = \frac{F}{m}$$
Circuits. He does the identical move to Ohm’s Law. $V=IR$ gets solved for whichever variable is missing, with no regard for which one is doing the causing. Rewritten as $I=V/R$, it reads the same way the mechanics case does: a voltage (the cause) produces current flow (the effect), throttled by however much resistance stands in the way.
$$V=IR \quad\longrightarrow\quad I = \frac{V}{R}$$
One pattern, mapped directly: force is to voltage what acceleration is to current, and mass is to resistance — cause, effect, and whatever throttles the effect, the same triad showing up in two domains of physics usually taught as unrelated memorization burdens. Once you see it, force-and-mass and voltage-and-resistance stop looking like separate things to memorize and start looking like one idea, applied twice.
Catalog status: Proven Systems
Both laws are settled physics — Newton’s second law confirmed at everyday scales for over three centuries, Ohm’s Law the working foundation of circuit design for two. The only thing moving here is emphasis: from “solve for the missing variable” to “which one is causing which.”
Where this touches PBT
The mechanics half sits where Five Equations already left it: Paper 1 gives force a literal mechanical cause, and Papers 14–15 audit how far that reduction actually holds.
The circuit half is a real, open connection, not a solved one. Paper 3 already models current as directional particle flow through PBT’s medium, and the project’s magnetism research already leans on domain wall pinning — microstructure physically impeding flow — to explain why some materials resist magnetic change more than others. That’s the same shape of idea electrical resistance would need. But PBT has no derivation of Ohm’s Law or resistance itself yet — worth returning to, not a claim being made here.