A one-page summary of Force and Translational Dynamics — Newton's three laws, free-body diagrams, common forces, friction, springs, gravity, and circular motion.
Newton's Laws · 18–23% of the AP Physics 1 exam (the heaviest unit)
F_net = ma
F_g = mg
F_f = μF_N
a_c = v²/r
The basics
What's covered: Forces, Newton's three laws, free-body diagrams, gravity, normal force, friction, springs, and circular motion
Exam weight: 18–23% — the heaviest single unit on the exam
The big question: What causes objects to accelerate, stay at rest, or move at constant velocity?
The master equation: F_net = ma. Everything in Unit 2 is an application of this.
📐 Key equations
F_net = ma
Newton's second law. The net force on a system equals mass times acceleration. Acceleration points in the same direction as F_net.
F_g = mg
Weight near Earth. Gravitational force on a mass m. Use g = 10 m/s² (or 9.8 / 9.81 if specified).
F_g = Gm₁m₂/r²
Universal gravitation. Force between two masses. Inversely proportional to distance squared.
F_k = μ_k · F_N
Kinetic friction. Always opposes the direction of motion. Doesn't depend on contact area.
F_s,max = μ_s · F_N
Maximum static friction. Below this, static friction adjusts to whatever's needed to prevent slipping. μ_s > μ_k typically.
F_spring = kx
Hooke's law. Force a spring exerts is proportional to its displacement from equilibrium. Force points back TO equilibrium.
a_c = v²/r
Centripetal acceleration. For circular motion. Always points toward the center of the circle.
F_c = mv²/r
Centripetal force. The net inward force needed for circular motion. Provided by tension, gravity, friction, or normal force.
T = 2πr/v = 1/f
Period. Time for one revolution. Frequency f = 1/T.
The 9 topics at a glance
2.1 Systems & Center of Mass
A system is any group of objects chosen for analysis. The center of mass behaves like a single particle. Internal forces never change CoM motion — only external forces do.
2.2 Forces & Free-Body Diagrams
A force is an interaction. Free-body diagrams show every external force on an object as arrows from a single dot. Don't include forces the object exerts on OTHER objects.
2.3 Newton's Third Law & Tension
Forces come in equal-and-opposite pairs acting on DIFFERENT objects. In an ideal string, tension is the same throughout. Ideal pulleys are massless and frictionless.
2.4 Newton's First Law
If F_net = 0, velocity is constant (could be zero). This is translational equilibrium. Inertia (= mass) is the resistance to changes in motion.
2.5 Newton's Second Law
F_net = ma. Acceleration is proportional to net force, inversely proportional to mass. Same direction as net force. The master equation of mechanics.
2.6 Gravitational Force
F_g = Gm₁m₂/r² for any two masses. Near Earth: F_g = mg. Weight = gravitational force. Apparent weight = normal force on you (what a scale reads).
2.7 Friction
Kinetic friction: F_k = μ_k·F_N (opposes motion). Static friction: adjusts up to μ_s·F_N. Doesn't depend on contact area. μ_s usually > μ_k.
2.8 Spring Forces (Hooke's Law)
F_s = kx. Spring force is proportional to displacement from equilibrium, always pointing BACK toward equilibrium. Spring constant k measures stiffness.
2.9 Circular Motion
a_c = v²/r points to the center. F_c = mv²/r is the net inward force — provided by tension, gravity, friction, or normal. T² ∝ r³ for orbits.
Normal force (F_N): Perpendicular to a surface, pushing the object away from the surface. Adjusts to prevent passing through. NOT always equal to weight.
Tension (T): Pulling force through a string/rope/cable. Same throughout an ideal massless string.
Friction (F_f = μF_N): Parallel to a surface, opposing motion (kinetic) or attempted motion (static).
Spring force (F_s = kx): Restoring force from a stretched/compressed spring. Points toward equilibrium.
Applied force: Any push or pull from an external agent (person, motor, etc.).
📏 How to solve a Newton's-second-law problem
1. Draw a free-body diagram. Label every force on the object. One dot, arrows out.
2. Choose a coordinate system. Make one axis parallel to the acceleration if possible (e.g., parallel to an incline).
3. Decompose forces into components. Use sin and cos for forces at angles.
4. Apply F_net = ma in EACH direction. ΣF_x = ma_x and ΣF_y = ma_y. Be careful with signs.
5. Solve. Often you'll have two equations and two unknowns.
⚠️ Common exam traps
Newton's third law pairs act on DIFFERENT objects. The normal force on you and your weight aren't a third-law pair — they're both forces ON you.
Normal force ≠ weight on inclines, in elevators, or whenever applied forces push down on the object. Re-derive it from Newton's second law.
Friction doesn't depend on contact area. It only depends on μ and the normal force.
Static friction adjusts. Don't automatically use F_s = μ_s·F_N — that's only the MAXIMUM. Below the threshold, static friction equals whatever's needed to prevent slipping.
\"Centripetal force\" isn't a new force. It's a label for the net inward force, which comes from real forces like tension, gravity, friction, or normal.
Apparent weightlessness ≠ no gravity. Astronauts in orbit feel weightless because they're in free fall — gravity is still very much acting on them.
Mass vs. weight. Mass (kg) doesn't change with location; weight (N) does. On the Moon, your mass is the same but your weight is ~1/6.