Dynamics
This page covers the core ideas now; worked examples and practice problems will keep expanding.
1. Newton's Three Laws
Dynamics asks the question kinematics deliberately avoided: what causes motion to change? The answer, in three parts, is Newton's laws — and almost every dynamics mistake on the AP exam comes from misapplying one of these three, not from bad algebra.
First Law — Inertia
An object's velocity doesn't change unless a net external force acts on it. "At rest" and "moving at constant velocity" are physically the same state — neither requires a force to maintain.
Second Law — F = ma
Fnetnet force (N) — the vector sum of every force acting on an object.mmass (kg) — the object's resistance to acceleration.aacceleration (m/s²) — always in the same direction as the net force.
This is a statement about net force. If five forces act on an object, you add all five as vectors first — F = ma applies to the result, never to any single force in isolation.
Third Law — Action/Reaction
Forces come in pairs that act on two different objects, are equal in magnitude, and point in opposite directions. They never cancel each other out because they act on different bodies.
"If two objects push on each other with equal and opposite forces, nothing should move." False — those forces act on two different objects, so each object still responds to the force acting on it according to F = ma. Action-reaction pairs never cancel within a single free-body diagram.
2. Free-Body Diagrams
A free-body diagram isolates one object and draws every force acting on it as an arrow, with no forces from other objects included. The single most common source of error in this entire course is an incomplete or incorrect free-body diagram — get this step right and the math that follows is usually easy.
Standard forces to check for: gravity (always present, points down), normal force (perpendicular to the contact surface), tension (along a rope or string, pulling), friction (opposes relative sliding, parallel to the surface), and applied forces (anything explicitly pushing or pulling).
3. Friction
fsstatic friction — resists the start of motion, up to a maximum value.fkkinetic friction — acts on an object already sliding.μcoefficient of friction — depends on the two surfaces in contact, not on area or speed.Nnormal force (N) — friction is always proportional to this, not to weight directly.
"A heavier object always has more friction." Only true if weight increases the normal force directly (e.g., flat ground). On an incline, or when another force has a vertical component, normal force and weight are no longer the same thing — friction depends on N, not on mg alone.
4. Simulator
Predict the system's acceleration before you check: try different masses on each side and see how the acceleration changes.
5. Practice Problems
1. A 5.0 kg box is pushed across a floor with a 20 N horizontal force. If μk = 0.3, find the box's acceleration.
2. Two blocks (3 kg and 2 kg) are connected by a string over a frictionless pulley. Find the system's acceleration.