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AP Physics 1: Algebra-Based · Unit 2 of 8

Force and Translational Dynamics

Name: AP Physics 1: Algebra-Based Unit 2: Force and Translational Dynamics
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18–23% of the exam6 lessons · 85 min52 terms

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What this unit covers

The topics below follow the published Physics 1 course framework for Unit 2. This unit is worth 18–23% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Newton’s lawsFrictionFree-body diagramsCircular motion & gravitation

Lessons in this unit

Formulas in Unit 2

Newton’s second law

ΣF = ma

ΣF is the vector sum of all forces (newtons, N). Solve component by component: ΣF_x = ma_x and ΣF_y = ma_y.

Weight

W = mg

g = 10 m/s² here (AP tables use 9.8). Weight is a force in newtons; it is never measured in kilograms.

Weight components on an incline (angle θ)

along incline: mg sinθ · perpendicular: mg cosθ

On a ramp, gravity splits into a part that pulls the object down the slope (mg sinθ) and a part pressing it into the surface (mg cosθ).

Friction force

f_k = μ_k N · f_s ≤ μ_s N

On flat ground with no vertical push, N = mg. Static friction is an inequality: it only reaches its maximum right at the verge of slipping.

Centripetal acceleration and force

a_c = v² / r · F_c = mv² / r

Both point toward the center of the circle. Doubling the speed quadruples both, because v is squared.

Newton’s law of universal gravitation

F = G·m₁·m₂ / r²

G = 6.67 × 10⁻¹¹ N·m²/kg². The force is an inverse-square law: triple the separation and the force drops to one-ninth.

The two-step method

Step 1 (system): a = ΣF_external / Σm · Step 2 (one body): ΣF on that body = m_that body · a

Step 1 gives the acceleration. Step 2 uses that acceleration to solve for the internal force.

Block on a frictionless incline

along: mg sin θ = ma → a = g sin θ · perpendicular: N = mg cos θ

The acceleration down a frictionless incline is independent of mass — the same reason all objects fall together.

Newton's second law for circular motion

ΣF_toward center = m v² / r

Sum the *real* forces, taking toward-the-center as positive. Then set that sum equal to mv²/r.

Circular orbit

GMm/r² = mv²/r → v = √(GM/r) · T = 2π√(r³/GM)

The orbiting mass m cancels: orbital speed and period depend only on the central mass and the radius, never on the satellite.

Every term in Unit 2

All 52 terms we publish for Force and Translational Dynamics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Newton's second law: ΣF = ma, applied separately along each axis. Acceleration is in the direction of the NET force, not of any single force.
Weight vs mass: Mass is the amount of matter and is frame-independent; weight is the gravitational force mg and changes with location.
Newton's third law: Forces come in equal and opposite pairs acting on DIFFERENT objects. The two never cancel, because they are not on the same body — which is why a horse can pull a cart.
Centripetal acceleration: a_c = v²/r directed toward the center of the circular path, caused by whatever real force points inward — tension, friction, gravity, or the normal force.
Static vs kinetic friction: Static friction adjusts up to μsN to prevent sliding; kinetic friction is μkN and constant once sliding. μs is generally larger than μk.
Friction direction: Opposes relative sliding between the surfaces, which is not always opposite the object's motion — friction propels a walking person forward.
Inclined plane components: Weight resolves into mg sin θ along the incline and mg cos θ perpendicular to it, so the normal force is mg cos θ.
Uniform circular motion: Speed is constant but velocity changes direction, so there is a centripetal acceleration a = v²/r directed toward the center.
Centripetal force: Not a new force — it is the name for whatever real force points to the center: tension, gravity, friction or normal force.
Newton's law of gravitation: F = Gm₁m₂/r², where r is measured center to center. Doubling the separation quarters the force.
Orbital motion: Gravity supplies the centripetal force, so Gm₁m₂/r² = mv²/r. Orbital speed depends on the central mass and radius, not the orbiting mass.
Apparent weight: The normal force a scale reads. It exceeds mg when accelerating upward and falls to zero in free fall.
Identifying third-law pairs: The pair to "Earth pulls ball down" is "ball pulls Earth up", not "ground pushes ball up". Swap the two objects and reverse the direction.
Why the normal force is not always mg: It equals mg only when the surface is level and there is no vertical acceleration or other vertical force. In a lift or on an incline it is not.
Connected objects: Treat the system as one body to find acceleration, then isolate one body to find the internal force between them.
Banked curve: On a frictionless banked curve, the horizontal component of the normal force supplies the centripetal force, so the required angle depends on speed and radius.
Vertical circular motion: At the top, gravity and any tension both point to the center. The minimum speed to maintain contact is where the normal force just reaches zero.
Free-body diagram errors: The commonest are drawing a "force of motion" in the direction of travel, and including centripetal force as a separate arrow alongside the real force causing it.
Static equilibrium: ΣF = 0 in every direction and Στ = 0 about every axis. Both conditions are required; forces alone are not sufficient for an extended body.
Inertial mass vs gravitational mass: Inertial mass resists acceleration, gravitational mass determines weight. They are experimentally identical, which underlies general relativity.
Force as the slope of momentum: Net force is the rate of change of momentum, so a force-time graph's area gives the momentum change directly.
Why heavier objects do not fall faster: Doubling mass doubles the gravitational force but also doubles the inertia resisting it, so a = F/m = g regardless of mass.
Newton's first law: An object at rest stays at rest and one in motion continues at constant velocity unless acted on by a net external force. Defines what a force does: change motion, not maintain it.
Inertia: An object's resistance to a change in motion, measured by its mass. Not a force, and not something an object "has more of" when moving faster.
Identifying a third-law pair: Swap the two nouns: "Earth pulls the book down" pairs with "the book pulls Earth up". If both forces act on the same object, it is not a third-law pair.
Free-body diagram: A dot for the object with every force acting ON it drawn as an arrow from the dot. Forces the object exerts on other things never appear.
Weight: The gravitational force on an object, W = mg. A force in newtons, not a property in kilograms, and it changes with location while mass does not.
Normal force: The perpendicular contact force from a surface. It equals mg only on a level surface with no vertical acceleration and no other vertical forces — which is a special case, not the definition.
Normal force on an incline: N = mg cos θ, because only the perpendicular component of weight presses into the surface. The parallel component mg sin θ is what accelerates the object down the slope.
Why static friction is not always μₛN: μₛN is its MAXIMUM. Below that, static friction equals whatever is needed to prevent motion — a block sitting still on a slope has friction equal to mg sin θ, not to μₛN.
Direction of friction: Opposes relative sliding at the surface, not necessarily the motion of the object. Friction drives a car forward, which is why "friction always opposes motion" is a trap.
Tension: The pull transmitted along a rope, equal throughout an ideal massless rope over a frictionless pulley. Two different tensions in one continuous ideal rope is a setup error.
Spring force (Hooke's law): F = −kx, proportional to displacement from equilibrium and directed back toward it. The minus sign is the restoring direction, not a negative magnitude.
Equilibrium: Net force zero, so acceleration is zero. Includes constant velocity, not just rest — a car at steady speed is in equilibrium.
Systems and internal forces: Treating two connected objects as one system makes internal forces cancel, leaving only external forces. Fastest route to the acceleration of an Atwood machine or a block train.
Atwood machine: Two masses over a pulley: a = (m₁ − m₂)g / (m₁ + m₂). The system accelerates because the weights differ, and tension is between the two weights.
Elevator problems: The scale reads the normal force, not the weight. Accelerating up gives N > mg, accelerating down gives N < mg, and free fall gives N = 0.
Terminal velocity: Reached when drag equals weight, so net force and acceleration are zero and the speed stops increasing. Not zero velocity — constant velocity.
Uniform circular motion is accelerated motion: Speed is constant but direction changes, so velocity changes and there is acceleration — directed at the center.
Centripetal force is not a new force: It is the name for whatever real force points at the center: tension, gravity, friction, or the normal force. Naming that force is what the question is asking.
Newton's law of universal gravitation: F = Gm₁m₂/r². An inverse-square law, so tripling the separation cuts the force to a ninth.
Gravitational field strength: g = GM/r², the force per unit mass at a distance r from a mass M. Explains why g differs at altitude and on other planets.
Orbital speed: Setting gravity as the centripetal force gives v = √(GM/r). Independent of the orbiting object's mass, which is why a satellite and an astronaut orbit together.
Apparent weightlessness: In orbit, everything falls together, so the normal force is zero and objects float. Gravity is still acting — it is what curves the path.
The massless string assumption: An ideal string has no mass, so tension is the same at every point along it. Give the string mass and the tension differs end to end, which is why the assumption is stated rather than assumed silently.
The ideal pulley assumption: An ideal pulley is massless and frictionless, so it changes the direction of the tension without changing its magnitude. A pulley with mass requires a torque equation and the tensions on the two sides differ.
Net force determines acceleration, not velocity: An object with zero net force keeps whatever velocity it has, which may be large. Asking what the net force is tells you how the motion is CHANGING, never how fast the object is going.
A free-body diagram has no ma arrow: ma is the result of the forces, not one of them. Drawing it alongside the real forces double-counts and is the single most common free-body diagram error.
The coefficient of friction has no units: It is a ratio of two forces, so mu is a bare number. Any answer carrying newtons or kilograms in mu is a setup mistake.
Kinetic friction ignores speed and contact area: To the accuracy this course uses, f_k = mu_k N regardless of how fast the surfaces slide or how much of them touch. Doubling the contact patch does not double the friction.
Two blocks pushed together: the contact force: Treat both as one system to get the acceleration, then isolate ONE block to find the force between them. The contact force is not the applied force, and which block you isolate changes the algebra but not the answer.
Normal force is perpendicular by definition: It is the component of the surface's push that is perpendicular to the surface. On an incline it is perpendicular to the slope, not vertical, which is why it equals mg cos(theta) there.

What examiners penalize here

On the AP exam, "equilibrium" does not mean "at rest." An object moving at constant velocity has zero acceleration, so its net force is also zero. Constant velocity and rest are the *same* dynamical situation.
Draw the free-body diagram before writing a single equation. On free response, a correct FBD with properly labeled forces earns points even if your algebra later slips — and it prevents you from inventing forces that are not there.
Watch the difference between "is it moving yet?" and "how fast does it slow down?" Use **static** friction (an inequality, up to μ_s N) to test whether motion starts; use **kinetic** friction (a fixed μ_k N) once it is already sliding.
When a circular-motion problem asks for a force, first ask "which real force points toward the center?" Then set that force equal to mv²/r. Naming the actual force (tension, friction, gravity, normal) is what earns the reasoning point.
Draw a separate free-body diagram for each object, even when you plan to use the system shortcut. Rubrics award the diagrams independently of the algebra, and a labeled diagram with no numbers still earns points.
On any circular-motion free-response, write "toward the center is positive" and then sum only the real forces. If your equation contains a term called F_c alongside tension and weight, you have counted the same force twice.

Practice Physics 1

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

168 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 1 study guideAll units, weights and score data in one place All 8 Physics 1 unitsThe full course

Questions about this unit

How much of the AP Physics 1: Algebra-Based exam is Unit 2?

Unit 2, Force and Translational Dynamics, is worth 18–23% of the Physics 1 multiple-choice section according to the published course framework. Across all 8 units that makes it one of the heaviest units on the exam, and worth front-loading.

What topics are covered in Physics 1 Unit 2?

Force and Translational Dynamics covers Newton’s laws, Friction, Free-body diagrams and Circular motion & gravitation. We publish 52 terms with definitions for this unit, all of them on this page.

How should I study Physics 1 Unit 2?

Read the 6 lessons below first — about 85 minutes — then drill the 52 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 8 units of AP Physics 1: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 1: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.