Inside This Unit: The Full Breakdown
Dynamics connects forces to motion through Newton's three laws. This unit teaches you to identify forces, draw free-body diagrams, and apply F = ma to solve problems involving friction, tension, normal force, and gravity.
Why it matters
Newton's laws are the most heavily tested topic on the AP Physics 1 exam. Free-body diagrams and F = ma appear on virtually every free-response question. You must be able to analyze forces systematically and apply Newton's second law in multiple dimensions.
Key concepts
- Newton's First Law (inertia): An object remains at rest or in constant velocity unless acted upon by a net external force.
- Newton's Second Law: ΣF = ma — the net force on an object equals its mass times its acceleration.
- Newton's Third Law: Every action force has an equal and opposite reaction force acting on a different object.
- Free-body diagrams show all forces acting ON a single object and are the essential first step for every dynamics problem.
Newton's Laws of Motion
Newton's First Law states that an object will maintain its state of motion — at rest or moving at constant velocity — unless a net external force acts on it. This property is called inertia, and mass is the measure of an object's inertia. Newton's Second Law quantifies force: ΣF = ma, where ΣF is the vector sum (net force) of all forces acting on an object. If the net force is zero, the object is in equilibrium (either at rest or moving at constant velocity). Newton's Third Law states that forces always come in pairs: if object A pushes on object B with a force, object B pushes back on A with an equal force in the opposite direction. These third-law pair forces act on different objects and therefore never cancel each other.
Free-Body Diagrams and Force Analysis
Free-body diagrams (FBDs) are the most important tool in physics problem-solving. To draw one: isolate the object, represent it as a point, and draw arrows for every force acting ON it — weight (always downward, mg), normal force (perpendicular to the contact surface), friction (parallel to the surface, opposing relative motion or tendency of motion), tension (along a rope or string, pulling away from the object), and any applied forces. Do not include reaction forces that act on other objects. After drawing the FBD, choose a coordinate system (often tilted to align with motion on inclined planes), resolve forces into components, and apply ΣF = ma in each direction independently. Setting up the FBD correctly is worth significant partial credit on AP free-response questions even if you make algebra errors afterward.
Friction and Applications
Friction is a contact force that opposes relative motion between two surfaces. Static friction (fₛ ≤ μₛN) prevents an object from starting to move and adjusts its magnitude up to a maximum value determined by the coefficient of static friction (μₛ) and the normal force (N). Kinetic friction (fₖ = μₖN) acts on an object that is already sliding and has a constant magnitude. The coefficient of kinetic friction is typically less than the coefficient of static friction. On inclined planes, the weight component parallel to the surface (mg sin θ) drives the object downhill, while the normal force equals mg cos θ (not mg). Atwood machines, connected blocks, and pulley systems all involve applying Newton's second law to multiple objects simultaneously, treating the system's net force as driving the entire system's acceleration.
AP exam tip
On the AP exam, always draw a complete free-body diagram before writing any equations. Label every force with its name (not just an arrow). On inclined plane problems, tilt your axes to align with the surface — it simplifies the component decomposition significantly.
Connections to other units
- Unit 1 (Kinematics): Once you find acceleration from F = ma, you use kinematic equations to describe the resulting motion.
- Unit 3 (Circular Motion): Circular motion requires a centripetal force, which is a specific application of Newton's second law.
- Unit 7 (Torque): Rotational dynamics extends F = ma to τ = Iα for rotating objects.
