AP Physics 1 Unit 2 ReviewForce and Translational Dynamics

AP Physics 1 Unit 2, Force and Translational Dynamics, is where you learn what makes objects speed up, slow down, or stay put. The single biggest idea is Newton's second law, which says the acceleration of a system's center of mass equals the net force divided by the system's mass. Everything in the unit, from friction to spring forces to circular motion, is really just a different ingredient you plug into that one equation. At 18-23% of the exam, this is the heaviest-weighted unit in the course, and the free-body diagram skills you build here show up in nearly every later unit.

What this unit covers

Systems, center of mass, and what counts as "the object"

• A system is whatever collection of objects you decide to analyze together. If the internal details don't matter for the question, you can treat the whole system as a single object.
• The center of mass is the balance point of a system. For symmetric objects it sits on lines of symmetry, and for a set of point masses you compute it with $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$.
• This matters because Newton's laws technically describe the motion of a system's center of mass. Internal forces (objects in the system pushing on each other) cannot change the center of mass's motion. Only external forces can.

Forces and free-body diagrams

• A force is always an interaction between two objects or systems. Nothing exerts a force on itself, and every force you draw should have a clear "exerted by" and "exerted on."
• Contact forces (normal force, friction, tension) are the macroscopic result of interatomic electric forces between touching surfaces. Long-range forces like gravity act without contact.
• A free-body diagram shows every force the environment exerts on one chosen object or system, drawn as vectors starting from a dot at the center of mass. You never include forces the object exerts on other things.
• The free-body diagram is the translation step. You read a scenario, draw the diagram, and the diagram hands you the equations. Almost every force problem starts here.

Newton's three laws

• First law: if the net force on a system is zero, its velocity stays constant. That includes sitting still and moving at constant velocity. Both are translational equilibrium, where $\sum \vec{F} = 0$.
• Second law: $\vec{a}_{sys} = \frac{\vec{F}_{net}}{m_{sys}}$. Acceleration points the same direction as the net force, and its size is proportional to the net force and inversely proportional to mass.
• Third law: when A pushes on B, B pushes back on A with a force equal in magnitude and opposite in direction, $\vec{F}_{A\text{ on }B} = -\vec{F}_{B\text{ on }A}$. The two forces in a pair always act on different objects, so they never cancel each other on a single free-body diagram.
• Forces can be balanced in one direction and unbalanced in another. A box sliding across a floor can be in vertical equilibrium while accelerating horizontally.

The specific forces you'll calculate

• Gravity between any two masses follows Newton's law of universal gravitation, $F_g = G\frac{m_1 m_2}{r^2}$. Near Earth's surface this simplifies to weight, $F_g = mg$.
• Kinetic friction acts when surfaces slide past each other, opposes the relative motion, and has magnitude $F_{f,k} = \mu_k F_n$. It does not depend on contact area.
• Static friction acts when surfaces are not sliding. It adjusts to whatever value prevents slipping, up to a maximum, so $|F_{f,s}| \leq \mu_s F_n$. It is an inequality, not a fixed value.
• An ideal spring exerts a restoring force proportional to how far it is stretched or compressed from its relaxed length, following Hooke's law, $F_s = -k\Delta x$.
• Tension is the net result of segments of a string or cable pulling on each other. For an ideal (massless) string, tension is the same throughout.

Circular motion and orbits

• An object moving in a circle at constant speed is still accelerating, because the direction of its velocity keeps changing. That centripetal acceleration points toward the center with magnitude $a_c = \frac{v^2}{r}$.
• "Centripetal force" is not a new kind of force. It is whatever real force (gravity, tension, friction, normal force) happens to point toward the center of the circle.
• For a satellite in circular orbit, gravity alone provides the centripetal acceleration. Setting gravitational force equal to $ma_c$ gives Kepler's third law for circular orbits, $T^2 = \frac{4\pi^2}{GM}R^3$, which links orbital period to orbital radius and the central body's mass.

Unit 2, Force and Translational Dynamics at a glance

Why Unit 2, Force and Translational Dynamics matters in AP Physics 1

Unit 1 told you how to describe motion. Unit 2 tells you why motion happens, and that cause-and-effect reasoning is the backbone of the whole course. The skill of choosing a system, drawing a free-body diagram, and translating it into Newton's second law is the most reused move in AP Physics 1.

• This unit builds the course's core theme of force interactions, the idea that forces always come in pairs between two objects and that only external forces change a system's motion.
• It develops your fluency with multiple representations. You constantly translate between a written scenario, a free-body diagram, an equation, and a motion graph, which is exactly what the exam rewards.
• The systems and center-of-mass thinking introduced here is what later lets you decide when energy or momentum is conserved, since that decision hinges on identifying external versus internal forces.

How this unit connects across the course

• Kinematics (Unit 1) gives you the acceleration vocabulary that Newton's second law explains. A typical problem chains them together, so you find $a$ from forces, then use kinematics to find velocity or position.
• Work and energy (Unit 3) reuses every force from this unit. Work is force times displacement, gravitational force becomes gravitational potential energy, and the spring force from Hooke's law becomes spring potential energy.
• Momentum (Unit 4) is built directly on Newton's second and third laws. Impulse is net force acting over time, and the third-law force pairs you draw here are exactly why momentum is conserved in collisions.
• Torque and rotation (Units 5 and 6) are the rotational remix of this unit. Newton's second law becomes $\tau_{net} = I\alpha$, and free-body diagrams grow into diagrams that also track where each force acts. Spring forces return as the restoring force behind oscillations (Unit 7), and buoyant and pressure forces in fluids (Unit 8) get analyzed with the same free-body diagram method.

Key equations and processes

• $\vec{a}_{sys} = \frac{\vec{F}_{net}}{m_{sys}}$ is Newton's second law, your main tool for connecting forces to acceleration.
• $\sum \vec{F} = 0$ defines translational equilibrium, the condition for constant velocity (Newton's first law).
• $\vec{F}_{A\text{ on }B} = -\vec{F}_{B\text{ on }A}$ is Newton's third law, used to relate forces between interacting objects.
• $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$ locates the center of mass of a system of objects along an axis.
• $F_g = G\frac{m_1 m_2}{r^2}$ gives the gravitational force between any two masses; $F_g = mg$ is the near-surface shortcut.
• $F_{f,k} = \mu_k F_n$ gives kinetic friction once surfaces are sliding.
• $|F_{f,s}| \leq \mu_s F_n$ caps static friction; use the maximum only when something is on the verge of slipping.
• $F_s = -k\Delta x$ is Hooke's law for an ideal spring, with the negative sign showing the force is restoring.
• $a_c = \frac{v^2}{r}$ gives centripetal acceleration for circular motion at speed $v$ and radius $r$.
• $T^2 = \frac{4\pi^2}{GM}R^3$ relates a circular orbit's period to its radius and the central mass (Kepler's third law).
• Process to know cold: define the system, draw the free-body diagram, pick axes (tilt them along an incline), write $\sum F = ma$ for each axis, then solve. This sequence is the unit.

Unit 2, Force and Translational Dynamics on the AP exam

At 18-23% of the exam, this is the most heavily weighted unit in AP Physics 1, and its skills bleed into questions from every other unit. Multiple-choice questions ask you to pick the correct free-body diagram for a scenario, rank net forces or accelerations across cases, identify third-law force pairs, and reason about how changing mass, angle, or coefficient of friction changes the outcome. Free-response questions lean on this unit hard. You might draw a free-body diagram as part (a) of a question, derive an expression for acceleration or tension in terms of given symbols, or design an experiment to measure a coefficient of friction or a spring constant from a graph's slope. Expect to justify claims in words, not just compute, especially explaining why static friction or the normal force takes a particular value, or why an object in circular motion accelerates even at constant speed. Multi-step problems often blend this unit with kinematics, so practice finding acceleration from forces and then feeding it into the equations of motion.

Essential questions

• Why does an object's motion change, and why does it sometimes not change even when forces act on it?
• If every force has an equal and opposite partner, how does anything ever accelerate?
• When can a messy collection of objects be treated as a single point at its center of mass, and when does that model break down?
• What real force keeps an object moving in a circle, and what happens if that force disappears?

Key terms to know

• System: a chosen collection of objects analyzed together, which can be treated as a single object when internal details don't matter.
• Center of mass: the mass-weighted average position of a system, the point whose motion Newton's laws actually describe.
• Free-body diagram: a sketch showing all external forces on one object as vectors starting from a dot at its center of mass.
• Net force: the vector sum of all forces exerted on a system, the quantity that determines acceleration.
• Translational equilibrium: the condition where the net force is zero, so velocity stays constant.
• Inertia: a system's resistance to changes in velocity, measured by its mass.
• Normal force: the contact force a surface exerts perpendicular to itself, with whatever magnitude the situation requires.
• Tension: the pulling force transmitted through a string, cable, or chain, uniform throughout an ideal string.
• Coefficient of friction: the unitless ratio relating friction force to normal force, with separate static ($\mu_s$) and kinetic ($\mu_k$) values.
• Hooke's law: the rule that an ideal spring's force is proportional to its stretch or compression and points back toward the relaxed length.
• Centripetal acceleration: the center-pointing acceleration of an object in circular motion, equal to $v^2/r$.
• Newton's law of universal gravitation: the attractive force between any two masses, proportional to both masses and inversely proportional to the square of their separation.
• Internal vs. external force: forces between objects inside a system (which can't move the center of mass) versus forces from the environment (which can).

Common mix-ups

• Third-law pairs never appear on the same free-body diagram. The normal force on a book and the book's weight are NOT a third-law pair; they act on the same object and just happen to balance. The true pair of the normal force is the book pushing down on the table.
• The normal force is not automatically $mg$. On an incline it is $mg\cos\theta$, and in an accelerating elevator it changes with the acceleration. Always solve for it from Newton's second law instead of assuming.
• Static friction is an inequality. Writing $F_{f,s} = \mu_s F_n$ for a box sitting calmly on a ramp is wrong unless the box is on the verge of slipping. Static friction only takes the value needed to prevent sliding.
• Centripetal force is not an extra arrow on your free-body diagram. Draw only real forces (gravity, tension, normal, friction), then set their center-pointing components equal to $\frac{mv^2}{r}$.