Force
An interaction between two objects that can change motion. A vector (has magnitude and direction). Measured in newtons (N). An object cannot exert a net force on itself.
FoundationNewton (N)
The SI unit of force. 1 N = 1 kg·m/s² (the force needed to accelerate a 1 kg mass at 1 m/s²). Near Earth, a 1 kg mass weighs about 10 N.
FoundationSystem
A group of one or more objects chosen for analysis. Forces between objects within the system are "internal"; forces from outside are "external." Only external forces change the system's center-of-mass motion.
2.1 Systems & Center of MassCenter of Mass
The single point at which all the mass of a system can be considered concentrated for analyzing translational motion. For symmetric objects, it's on the symmetry line. Calculated as x_cm = Σmᵢxᵢ / Σmᵢ.
2.1 Systems & Center of MassInternal vs External Forces
Internal forces act between parts of the system; external forces come from outside. Internal forces always come in third-law pairs that cancel, so they cannot change the system's center-of-mass motion. Only external forces matter.
2.1 Systems & Center of MassFree-Body Diagram (FBD)
A sketch showing every force acting ON a single object, drawn as labeled arrows from a dot (representing the center of mass). Each arrow points in the direction the force pushes or pulls. The single most important tool in Unit 2.
2.2 Free-Body DiagramsContact Force
A force that requires two objects to be touching (normal force, friction, tension, applied push/pull, spring). The opposite of a non-contact force like gravity, which acts at a distance.
2.2 Free-Body DiagramsNormal Force
The push a surface exerts perpendicular to itself on whatever is touching it. Symbol: F_N or N. It's NOT always equal to weight — it adjusts to whatever value is needed to prevent objects from passing through the surface.
2.2 Free-Body DiagramsNewton's Third Law
If object A exerts a force on object B, then B exerts an equal-magnitude, opposite-direction force back on A. The two forces act on DIFFERENT objects — they don't cancel each other out (they can't, because they're on different free-body diagrams).
2.3 Newton's Third LawAction-Reaction Pair
Two forces that satisfy Newton's third law. They have equal magnitude, opposite directions, are the same type of force (e.g., both gravitational), and act on different objects. Common student mistake: confusing third-law pairs with balanced forces on a single object.
2.3 Newton's Third LawTension
The pulling force transmitted through a rope, string, cable, or chain. In an ideal (massless) string, tension is the same throughout. An ideal pulley is massless and frictionless, so it doesn't change the tension — only the direction.
2.3 Newton's Third LawNewton's First Law (Inertia)
If the net force on a system is zero, its velocity stays constant (either at rest or moving with constant velocity). Inertia is the tendency of objects to resist changes in motion. Mass is the measure of inertia.
2.4 Newton's First LawTranslational Equilibrium
When the vector sum of all forces on a system is zero. The system can be at rest OR moving at constant velocity — both count as equilibrium. Forces can be balanced in one direction but unbalanced in another; the object accelerates only in the unbalanced direction.
2.4 Newton's First LawNewton's Second Law
F_net = ma. The acceleration of a system equals the net external force divided by the system's mass, and points in the direction of the net force. The cornerstone equation of mechanics.
2.5 Newton's Second LawNet Force
The vector sum of all forces acting on a system. Symbol: F_net or ΣF. If forces are in different directions, add them as vectors (or by components). Only the net force matters for acceleration.
2.5 Newton's Second LawUniversal Gravitation
Newton's law of universal gravitation: F_g = Gm₁m₂/r². The gravitational force between two masses is proportional to each mass and inversely proportional to the square of the distance between their centers. Always attractive; acts along the line connecting the centers.
2.6 Gravitational ForceWeight
The gravitational force on an object from a nearby astronomical body. Near Earth: F_g = mg, where g ≈ 10 m/s². Weight is a FORCE (in newtons), not a mass. Your mass is the same on the Moon; your weight is much less.
2.6 Gravitational ForceApparent Weight
The magnitude of the normal force on a system — what a scale would read. In an accelerating elevator, apparent weight differs from actual gravitational force. You feel "heavier" when accelerating up, "lighter" when accelerating down, and "weightless" in free fall.
2.6 Gravitational ForceGravitational Field
The region around a mass where another mass would feel a gravitational pull. Field strength g = F_g/m (units: N/kg). Near Earth's surface, g ≈ 10 N/kg, which is numerically equal to the acceleration due to gravity (10 m/s²).
2.6 Gravitational ForceEquivalence Principle
An observer in an accelerating reference frame cannot distinguish between the effects of acceleration and the effects of a gravitational field. Standing in an elevator accelerating upward at 10 m/s² feels identical to standing on Earth.
2.6 Gravitational ForceKinetic Friction
The friction force between two surfaces sliding past each other. Always opposes the relative motion. Magnitude: F_k = μ_k · F_N. The kinetic friction coefficient (μ_k) depends on the materials but not on speed or contact area.
2.7 FrictionStatic Friction
The friction force between surfaces that are NOT sliding past each other. Static friction adjusts to whatever value is needed to keep the object from slipping — up to a maximum (F_s,max = μ_s · F_N). Once the applied force exceeds this max, the object starts sliding.
2.7 FrictionCoefficient of Friction (μ)
A dimensionless number describing how "sticky" two surfaces are. Higher μ = more friction. The static coefficient (μ_s) is usually larger than the kinetic coefficient (μ_k), which is why it takes more force to START an object sliding than to keep it sliding.
2.7 FrictionHooke's Law
The force exerted by an ideal spring is proportional to its displacement from equilibrium: F_s = -kx (or magnitude F_s = k|x|). The negative sign means the force always points back toward equilibrium — that's why springs are "restoring."
2.8 Spring ForcesSpring Constant (k)
The stiffness of a spring. Units: N/m. A high k means a stiff spring (large force per unit stretch); a low k means a soft spring. The spring constant is a property of the spring itself, not of how you use it.
2.8 Spring ForcesCentripetal Acceleration
The acceleration of any object moving in a circle, always pointing toward the center. Magnitude: a_c = v²/r, where v is tangential speed and r is the radius. Even an object moving at constant speed in a circle is accelerating because its direction is changing.
2.9 Circular MotionCentripetal Force
The NET inward force that produces centripetal acceleration. F_c = mv²/r. It's NOT a new kind of force — it's a role played by existing forces: tension for a ball on a string, gravity for an orbit, friction for a car turning, normal force on a banked curve.
2.9 Circular MotionPeriod and Frequency
Period (T) is the time for one full revolution; frequency (f) is the number of revolutions per second. T = 1/f. For circular motion at constant speed: T = 2πr/v. Units: T in seconds, f in hertz (Hz, or 1/s).
2.9 Circular Motion