AP Physics 1 · Unit 2 of 8

Unit 2: Force and Translational Dynamics

18-23% of the multiple-choice section9 topics

Topics in this unit

Unit 2 (Force and Translational Dynamics) is the heaviest unit on the AP Physics 1 exam at 18 to 23% of the multiple-choice section. It covers topics 2.1 to 2.9: systems, free-body diagrams, Newton's three laws, gravitation, friction, springs, and circular motion.

AP Physics: Unit 2 (topics 2.1 Systems and Center of Mass, 2.2 Forces and Free-Body Diagrams, 2.3 Newton's Third Law, 2.4 Newton's First Law, 2.5 Newton's Second Law, 2.6 Gravitational Force, 2.7 Kinetic and Static Friction, 2.8 Spring Forces, 2.9 Circular Motion). Covers Unit 2 of the current AP Physics 1 course, weighted 18 to 23% of the multiple-choice section. AP Physics C: Mechanics has the same unit at 20 to 25% weighting, with an added topic on resistive forces.

The heaviest unit on the exam

Unit 2, Force and Translational Dynamics, is worth 18 to 23% of the multiple-choice section, the largest share on the AP Physics 1 exam (tied with Unit 3, Work, Energy, and Power). Nine topics, 2.1 through 2.9, take you from defining a system to circular motion, and nearly all of them get tested through the same skill: drawing a correct free-body diagram and turning it into $F_{net} = ma$ .

The unit also carries forward. Energy methods in Unit 3, momentum in Unit 4, and torque in Unit 5 all assume you can identify the forces acting on an object without hesitation. If you only have time to over-prepare one unit, make it this one.

Topics 2.1 to 2.5: systems, forces, and Newton's laws

The first five topics build the machinery. Topic 2.1 (Systems and Center of Mass) teaches you to decide what counts as the object: a single block, or two blocks plus the string between them treated as one system. Topic 2.2 (Forces and Free-Body Diagrams) is the core skill of the whole course; the guide on how to draw a free-body diagram walks through the rules step by step.

The CED then covers the laws in an unusual order: Newton's third law (2.3) comes before the first (2.4) and second (2.5). The ordering is deliberate. Identifying interaction pairs comes before analyzing equilibrium, and equilibrium is just the special case where the net force equals zero.

Topics 2.6 to 2.8: gravity, friction, and springs

Topic 2.6 covers gravitational force near Earth's surface ( $F_g = mg$ with $g = 9.8 \text{ m/s}^2$ ) and between any two masses, using $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$ .

Topic 2.7 (Kinetic and Static Friction) is the most tested trap in the unit. The formula sheet gives one line, $|F_f| \leq |\mu F_N|$ , an inequality that covers both cases: kinetic friction sits at the maximum value, while static friction takes whatever value keeps the object from sliding, up to that maximum. Because friction depends on the normal force, how to find normal force is a prerequisite, and the normal force is not always $mg$ .

Topic 2.8 covers spring forces with $F_s = -k\Delta x$ . The negative sign means the force opposes the stretch or compression, not that the force is literally negative.

Topic 2.9: circular motion

Circular motion closes the unit, and it is still a Newton's second law problem. An object moving in a circle at constant speed accelerates toward the center with $a_c = v^2/r$ , so the net force must also point toward the center.

The most common error is adding a centripetal force arrow to the free-body diagram as if it were a new force. Centripetal force is a role played by real forces (tension, gravity, friction, the normal force), and your diagram should show only those real forces. The centripetal force guide covers vertical circles, banked curves, and the classic apparent-weightlessness setup at the top of a loop, and the centripetal force calculator lets you check your numbers once the setup is done.

Free-body diagrams: the skill everything hangs on

Every topic in this unit funnels through the free-body diagram. A reliable process: draw the object as a dot or box, draw one labeled arrow for each force acting on the object (each arrow starting on it), and never include forces the object exerts on other things. Components of a force do not get their own arrows either; resolve them in your algebra, not in the diagram.

If the diagram is right, the algebra is bookkeeping. If it is wrong, nothing after it can save the answer. Practice with the free-body diagram builder, which lets you construct diagrams for common setups, and read the full walkthrough in how to draw a free-body diagram before your first unit test.

How Unit 2 shows up on the exam

At 18 to 23% of the multiple-choice section, Unit 2 works out to roughly 8 to 10 of the 42 questions. The free-response section has four questions (Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, and Qualitative/Quantitative Translation), and dynamics content can appear in any of them: a Mathematical Routines question might chain friction into kinematics, while an Experimental Design question might ask you to plan a measurement of a coefficient of friction.

A calculator is allowed on both sections, so arithmetic is not the bottleneck; setting up the correct equations is. The inclined plane simulator is built for exactly that setup practice: change the angle and the friction coefficient and watch how the force balance responds.

The five traps that cost the most points

These are the errors that show up most often in student work.

The normal force is not automatically $mg$ . On inclines, in accelerating elevators, or when a rope pulls at an angle, it changes. See how to find normal force.
Static friction is an inequality. Writing friction as its maximum value for a stationary object on level ground with nothing pushing it is wrong; the friction force there is zero.
Third law pairs never cancel, because they act on different objects. The pair of the table pushing up on a book is the book pushing down on the table, not gravity.
Mass is not weight. Mass $m$ is in kilograms; weight $F_g = mg$ is in newtons. A 5.0 kg object weighs 49 N.
Centripetal force is not an extra arrow on a free-body diagram. Only real forces go on the diagram.

Where to practice, and what comes next

Work the unit in this order: master free-body diagrams first, then net force problems on level ground, then inclines with the inclined plane problems guide and the inclined plane simulator, and circular motion last. When strings and pulleys show up in multi-object problems, how to find tension covers the standard setups.

The net force calculator and friction calculator are useful for checking homework against your hand work. Once forces feel solid, move on to Unit 3: Work, Energy, and Power, the other 18 to 23% unit, which leans on everything here.

Block sliding down a rough incline

A 4.0 kg block slides down a ramp inclined at $30^\circ$ above the horizontal. The coefficient of kinetic friction between the block and the ramp is $\mu_k = 0.20$ . Find the block's acceleration.

Find the weight and split it into components along and perpendicular to the incline. Weight: $F_g = mg = 4.0 \text{ kg} \times 9.8 \text{ m/s}^2 = 39.2 \text{ N}$ . Along the incline: $F_g \sin 30^\circ = 39.2 \times 0.500 = 19.6 \text{ N}$ . Perpendicular: $F_g \cos 30^\circ = 39.2 \times 0.866 = 33.9 \text{ N}$ .
Apply Newton's second law perpendicular to the incline. The block does not accelerate off the surface, so $F_N = 33.9 \text{ N}$ . Note that this is less than $mg = 39.2 \text{ N}$ .
Find the kinetic friction force, which points up the incline because the block slides down: $F_f = \mu_k F_N = 0.20 \times 33.9 \text{ N} = 6.78 \text{ N}$ .
Find the net force along the incline: $F_{net} = 19.6 \text{ N} - 6.78 \text{ N} = 12.8 \text{ N}$ , directed down the slope.
Apply Newton's second law along the incline: $a = F_{net}/m = 12.8 \text{ N} / 4.0 \text{ kg} = 3.2 \text{ m/s}^2$ .

The block accelerates at $3.2 \text{ m/s}^2$ down the incline. Quick check with the shortcut form: $a = g(\sin\theta - \mu_k \cos\theta) = 9.8 \times (0.500 - 0.20 \times 0.866) = 9.8 \times 0.327 = 3.2 \text{ m/s}^2$ . Same result.

Frequently asked questions

How much of the AP Physics 1 exam is Unit 2?

Unit 2 carries 18 to 23% of the multiple-choice section, the largest weighting in the course, tied with Unit 3 (Work, Energy, and Power). That works out to roughly 8 to 10 of the 42 multiple-choice questions, and dynamics content also appears throughout the free-response section.

What topics are in AP Physics 1 Unit 2?

Nine topics: 2.1 Systems and Center of Mass, 2.2 Forces and Free-Body Diagrams, 2.3 Newton's Third Law, 2.4 Newton's First Law, 2.5 Newton's Second Law, 2.6 Gravitational Force, 2.7 Kinetic and Static Friction, 2.8 Spring Forces, and 2.9 Circular Motion.

Is the friction equation on the AP Physics 1 formula sheet?

Yes, as a single inequality: the magnitude of the friction force is less than or equal to the coefficient of friction times the normal force. One line covers both cases. Kinetic friction equals that maximum; static friction can be anything from zero up to it. There is no separate static and kinetic equation on the sheet.

Do Newton's third law force pairs cancel each other out?

No. The two forces in a third law pair act on different objects, so they never appear on the same free-body diagram and can never cancel. When forces do cancel on one object, that is Newton's first or second law at work (net force zero), not the third law.

Is this unit different in AP Physics C: Mechanics?

The unit has the same title in AP Physics C: Mechanics but is weighted 20 to 25% there and adds a topic on resistive forces, analyzed with calculus. The Physics 1 version stays algebra-based and stops at circular motion.