Free particle in 2D

A point with no force on it. Drag it, give it a velocity, watch it drift.

Before we add forces, before springs or gravity or charges, there is one piece of physics so small it seems almost like nothing happens: a point with mass, alone in empty space, no force acting on it.”Free” here just means unconstrained. The particle has no potential energy function, no obstacle, no field pushing it around. Drag it to set its position, drag from the particle to set its velocity, and press start.

Without a force, the velocity is fixed. The particle traces a straight line forever, at constant speed.Newton’s first law: a body in motion stays in motion, in a straight line, unless acted upon by a force. The free particle is the lab demonstration of that law. This is the simplest non-trivial dynamical system — one integration step from initial conditions to all future states — and every more complex model is built on top of it. The two-body problem is two of these, with a force between them. A pendulum is one of these, with a string constraint and gravity. Most of classical mechanics is bookkeeping around this single idea.