Newton's Second Law: the net force on an object equals its mass times its acceleration.
Force is measured in newtons, where 1 N = 1 kg·m/s² — a newton is literally defined as exactly the force needed to accelerate 1 kg at 1 m/s². This single equation can be rearranged to solve for any of the three quantities, depending on which two you already know.
F in F = ma always means the net force — the sum of every force acting on the object, with correct signs, exactly like you practiced with free-body diagrams back in Lesson 2-1-1.
Build a list of every force acting along one line (like applied force and friction), pick a mass, and see the net force and resulting acceleration update live.
A 5 kg box is pushed with 20 N of applied force. Friction opposes the motion with 8 N. Find the box's acceleration.
For a fixed net force, doubling the mass exactly halves the acceleration. Tripling the mass cuts acceleration to a third. This is precisely the inertia idea from Lesson 2-1-2, now written as an exact proportion instead of a qualitative feeling.
Acceleration increases proportionally. Double the net force, double the acceleration.
Acceleration decreases proportionally. Double the mass, half the acceleration.
Here's a question that trips people up: if a bowling ball weighs so much more than a tennis ball, why do they hit the ground at the same time when dropped together (ignoring air resistance)?
The answer is hiding directly in F = ma. Weight itself is F_g = mg — it scales up exactly with mass. So when you solve for acceleration:
The mass cancels out of the equation completely. No matter how heavy an object is, gravity accelerates it at the same rate, g ≈ 9.8 m/s², because the force pulling on it and the mass resisting that pull grow together, in perfect proportion.
Adjust two very different masses and watch their weight change — but their acceleration under gravity alone never does.
Force does not directly control how fast something is moving. Force controls acceleration — the rate at which velocity changes.
Every dynamics problem for the rest of the year comes down to this same pattern: draw the FBD, find net force, apply F = ma. Lesson 2-2-3 raises the difficulty by tilting the surface — on an incline, even gravity has to be broken into components before you can find net force at all.