Unit 2 · Force and Translational Dynamics

System ● (core concept) — A collection of objects chosen for analysis together. A system's properties come from its objects and their interactions, and the system's internal structure affects how it is analyzed.

Center of mass ● (core concept) — The point at which an entire system can be modeled as a single object. For systems with symmetric mass distributions, it lies on the lines of symmetry.

Internal forces ● (core concept) — Interactions between objects within a chosen system. Internal forces do not influence the motion of the system's center of mass.

Force ● (core concept) — A vector quantity describing an interaction between two objects or systems. A force exerted on an object always comes from another object or system — an object cannot exert a force on itself.

Contact force ● (core concept) — A force exerted by direct touching. Macroscopically, contact forces are the effect of interatomic electric forces.

Free-body diagram ● (core concept) — A diagram showing each force exerted on a single object or system, drawn as vectors originating from a dot representing the center of mass. It is the tool for visualizing forces and writing the equations that describe the motion.

Newton's third law ● (core concept) — Interacting objects exert equal and opposite forces on each other: the force A exerts on B is equal in magnitude and opposite in direction to the force B exerts on A (F_A on B = −F_B on A).

Tension ● (core concept) — The force that segments of a string, cable, or chain exert on each other or on attached objects when pulled by an external force.

Ideal string and ideal pulley ○ — An ideal string has negligible mass, does not stretch, and has the same tension at every point. An ideal pulley has negligible mass and rotates about its center with negligible friction.

Net force ● (core concept) — The vector sum of all forces exerted on a system.

Translational equilibrium ● (core concept) — A configuration of forces in which the net force on a system is zero.

Newton's first law ● (core concept) — If the net force exerted on a system is zero, the system's velocity remains constant. Forces may be balanced in one direction while remaining unbalanced in another.

Newton's second law ● (core concept) — The acceleration of a system's center of mass is proportional to the net external force exerted on the system and points in the same direction as that net force (a_cm = F_net/m). Only a nonzero net external force changes the center-of-mass velocity.

Newton's law of universal gravitation ● (core concept) — The attractive gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass: F_g = G·m_1·m_2/r², directed along the line connecting them.

Gravitational field ● (core concept) — A model of how a mass affects the space around it without contact. Field strength g = F_g/m (in N/kg); when gravity is the only force on an object, its acceleration in m/s² numerically equals the field strength in N/kg. Near Earth's surface, g ≈ 10 N/kg.

Weight ● (core concept) — The gravitational force an astronomical body exerts on a relatively small nearby object: F_g = m·g.

Apparent weight ● (core concept) — What a scale actually reads: the magnitude of the normal force exerted on a system. It differs from mg when the system accelerates. A system appears weightless when gravity is the only force exerted on it, or when no forces act on it at all.

Inertial mass ● (core concept) — The property of an object that determines how much its motion resists changes when a force acts — the mass in Newton's second law.

Gravitational mass ● (core concept) — The property related to the gravitational attraction between two systems — the mass in the law of universal gravitation. It is experimentally verified to be equivalent to inertial mass.

Equivalence principle ● (core concept) — An observer in a noninertial reference frame cannot distinguish between an object's apparent weight and the gravitational force exerted on it by a gravitational field.

Kinetic friction ● (core concept) — Friction between two surfaces moving relative to each other, exerted opposite the direction of relative motion. Its magnitude is F_f,k = μ_k·F_n, independent of the contact area; the coefficient μ_k depends on the materials in contact.

Static friction ● (core concept) — Friction that prevents slipping between surfaces not moving relative to each other. It takes whatever value is needed to prevent sliding, up to a maximum of F_f,s,max = μ_s·F_n; μ_s is typically greater than μ_k for a given pair of surfaces.

Normal force ● (core concept) — The perpendicular component of the force a surface exerts on an object in contact with it, directed away from the surface.

Hooke's law ● (core concept) — An ideal spring (negligible mass) exerts a force proportional to its change in length from its relaxed length: F_s = k·x, always directed toward the equilibrium position of the object–spring system.

Centripetal acceleration ● (core concept) — The acceleration of an object in circular motion, directed toward the center of the circle: a_c = v²/r.

Centripetal force ● (core concept) — The net center-directed force that produces circular motion. It is not a separate force — it is supplied by real forces or their components, such as tension, static friction, the normal force, or gravity.

Tangential acceleration ● (core concept) — The rate at which an object's speed changes, directed tangent to the circular path. The net acceleration of an object in a circle is the vector sum of its centripetal and tangential accelerations.

Uniform circular motion ● (core concept) — Circular motion at constant speed, described by the period T (time for one full revolution) and the frequency f (revolutions per unit time), related by f = 1/T.

Kepler's third law ● (core concept) — For a satellite in circular orbit around a central body, the satellite's centripetal acceleration is caused only by gravitational attraction. The square of the orbital period is proportional to the cube of the orbital radius (T² = 4π²r³/(G·M)), so the period and radius are related to the mass of the central body. AP Physics 1 does not require Kepler's first or second laws.

Minimum speed at top of vertical loop ● (core concept) — At the top of a vertical circular loop, an object requires a minimum speed v = √(g·r) to maintain circular motion. At this minimum speed, the gravitational force is the only force causing the centripetal acceleration.

Conical pendulum ○ — A mass swinging in a horizontal circle on a string, where a component of the tension provides the centripetal force.

Banked turn ○ — A banked road curve where components of the normal force (and static friction) contribute the centripetal force. AP Physics 1 expects quantitative analysis of banked curves where no friction is required to maintain uniform circular motion; situations in which friction is required are treated qualitatively.