Physics · Mechanics · Module 4
Laws of Motion: What Changes Motion
Sixteen readings on where accelerations come from — the interactions that produce them, the diagrams that record them, and the friction and frames that complicate them.
Geometry tells us what motion is allowed; Newton tells us what motion occurs.
This module is being written. Parts marked coming are planned and not yet published. The order below is the order to read them in, and this page will be updated as each appears.
What this module is
Module 3 could describe any motion completely. Position, velocity and acceleration form a chain, and every problem in it was that chain under a different condition. But in all thirty-three of those posts the acceleration was given — stated, assumed, read off a graph, or produced by a constraint. Never explained.
This module explains it. The answer requires a new kind of object: not a property of one body, but an interaction between two. Everything here is that idea worked out — how to identify interactions, how to record them in a diagram that can be checked, and how to turn the diagram into equations that solve.
Results are derived, not quoted. Every formula is obtained rather than stated, and every one is given with the condition it depends on — which matters more here than in Kinematics, because the most common errors in dynamics are formulas applied where their condition has failed.
Start here
Work through in order the first time. Each part assumes the one before it, and several results are used later without being re-derived.
N1 — What Is a Force? coming
Why a body never carries a force, and what has to be named before any diagram can be drawn.
Coming from Module 3? The kinematics is assumed, not re-taught. K2, K13, K14 and K15 do the most work here.
The sixteen parts
The language first, then the diagram that carries it, then the situations where it is used.
The language of dynamics
N1 — What Is a Force? coming
Force is not motion. Force is interaction — and a body carries mass and velocity, never a force.
N2 — Newton’s First Law: Inertia and Frames coming
The first law does not describe bodies left alone. It tells you which frames the rest of the module may work in.
N3 — Newton’s Second Law coming
A law about the world, not a definition of force — and the constant-mass form is a special case, not the law.
N4 — Newton’s Third Law: Interaction Pairs coming
Why third-law partners never cancel in one body’s equation, and why the law is about one interaction rather than two forces.
The free-body diagram
N5 — Drawing the Free-Body Diagram coming
K2’s argument applied to forces: an arrow is a claim, and one body per diagram is not a stylistic preference.
N6 — Reading and Auditing Free-Body Diagrams coming
Find the error in someone else’s diagram. Nothing else on this site asks you to do that, and it is the rarer skill.
Applications
N7 — Equilibrium and Connected Bodies coming
Where K14’s constraints meet Newton: the geometry says what is allowed, the forces say what happens. Includes springs.
N8 — Inclined Planes coming
Choosing axes is not tidying up. It is the step that decides whether the algebra will work.
Friction
N9 — Static Friction coming
Static friction is self-adjusting. It satisfies an inequality, not an equation, and the equality holds only at the limit.
N10 — Kinetic Friction coming
Sliding, and the moment the static case stops applying.
N11 — Circular Motion and the Force That Supplies It coming
Centripetal force is a role, not a new interaction. Something physical must fill it — tension, friction, gravity, a normal reaction.
N12 — Which Body Slips First? coming
Friction as a competition between constraints, where the question is which one fails.
Systems
N13 — Two Blocks, One System coming
The forces on a body are not a fixed list. They depend on where you drew the boundary, and that is your choice.
N14 — Multi-Body and Multi-Constraint Systems coming Advanced
The high-level continuation of K14, where several constraints act at once and the geometry does most of the work.
Frames and synthesis
N15 — Non-Inertial Frames and Pseudo-Force coming Advanced
What to do when your frame is not inertial — and why the term you must add there is not a force in the sense N1 established.
N16 — Newtonian Motion in Complex Situations coming
Synthesis. No new physics; the student builds the whole model, and deciding what to model is the difficulty.
Worked examples
Five series, prepared alongside N5 rather than after N16 — because worked examples written late get shaped by whatever material happens to be left over.
A — Drawing forces. Identify what acts, correct a flawed diagram, choose the axes. Diagram-heavy, in the way K2’s set was.
B — Newton’s laws. One body, two bodies, and the system against the individual.
C — Friction. Static, limiting, block-on-block, inclined.
D — Constraints with dynamics. Pulley, multi-string, wedge.
E — Advanced. Non-inertial frames, multiple constraints, complex systems.
Practice
Six bands, from recognition to model construction. No answers are given — and no question names the part it comes from, because deciding that is most of the work.
NEET — recognition and direct application.
Engineering, standard — two-step: incline, connected blocks, simple pulley.
Engineering, difficult — where the representation matters: block-on-block, several equations at once.
JEE Main — mixed: pulley with incline, friction with acceleration, wedges.
JEE Advanced — model construction: multiple constraints, moving wedges, limiting cases. Do not start with a formula; start by deciding what system you are modelling.
Intuition — elementary problems where the physics can be seen before any algebra is written.
What comes after
Force is the first of three ways to ask the same question, and each of the next modules takes it somewhere the others cannot reach. Module 5 goes through work and energy, where the path stops mattering and only the endpoints remain. Module 6 goes through momentum, where F = dp/dt becomes the working tool and the rocket equation finds its home. Module 7 goes through torque, where a body stops being a particle and where a force is applied begins to matter.
Sixteen parts · five worked-example series · six practice papers · in progress · free, no sign-up
Every correction made to this module is listed on the corrections page.