| Term | Definition |
|---|---|
| center of mass | The point in a system where the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces. |
| constituent objects | The individual objects that make up a system. |
| differential mass | An infinitesimally small element of mass, denoted as dm, used in integration to calculate properties of nonuniform solids. |
| internal structure | The arrangement and organization of constituent parts within a system that affects how the system behaves and is analyzed. |
| lines of symmetry | Imaginary lines about which a system's mass distribution is balanced, and where the center of mass is located for symmetrical objects. |
| macroscopic system | A system large enough to be observed and analyzed at the scale of everyday objects, which can sometimes be treated as a single object. |
| mass density | The mass per unit length, area, or volume of a material or object, used to determine total mass through integration. |
| nonuniform solid | An object with varying mass density throughout its volume, requiring integration to determine its center of mass. |
| substructure | The internal organization and arrangement of components within a system that may change as external variables change. |
| symmetrical mass distribution | A distribution of mass in an object or system that is balanced about one or more lines or planes of symmetry. |
| system | A defined collection of objects whose energy and interactions are being analyzed. |
| system properties | The characteristics and behaviors of a system that are determined by the interactions between objects within it. |
| Term | Definition |
|---|---|
| banked surface | A tilted surface on which an object travels in a circular path, where components of normal force and friction contribute to centripetal acceleration. |
| centripetal acceleration | The acceleration directed toward the center of a circular path, required to keep an object moving in a circle. |
| circular orbit | The path of a satellite moving around a central body at a constant distance, where gravitational force provides the centripetal force needed to maintain the circular path. |
| conical pendulum | A pendulum that moves in a horizontal circular path, with tension providing a component of the centripetal force. |
| frequency | The number of complete oscillations or cycles of simple harmonic motion that occur per unit time, measured in hertz (Hz). |
| gravitational attraction | The force of attraction between two masses, which in orbital mechanics provides the centripetal force for circular orbits. |
| Kepler's third law | The relationship stating that the square of a satellite's orbital period is proportional to the cube of its orbital radius, expressed as T² = (4π²/GM)R³. |
| net acceleration | The vector sum of an object's centripetal acceleration and tangential acceleration. |
| normal force | The contact force exerted by a surface on an object perpendicular to that surface. |
| orbital period | The time required for a satellite to complete one full orbit around a central body. |
| orbital radius | The distance from the center of the central body to the satellite in a circular orbit. |
| period | The time required for an object to complete one full circular path, rotation, or cycle. |
| radius | The distance from the center of a circular path to the object moving along that path. |
| static friction | A friction force that acts between two surfaces in contact that are not moving relative to each other, preventing an object from slipping or sliding. |
| tangential acceleration | The rate at which an object's speed changes, directed tangent to the object's circular path. |
| tangential speed | The instantaneous speed of an object moving along a circular path, directed tangent to the circle. |
| tension | The macroscopic net force that segments of a string, cable, chain, or similar system exert on each other in response to an external force. |
| uniform circular motion | Motion of an object traveling in a circular path at constant speed. |
| vertical circular loop | A circular path oriented vertically, where an object must maintain a minimum speed at the top to continue circular motion. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces. |
| contact forces | Forces that result from two objects or systems physically touching each other, arising from interatomic electric forces. |
| coordinate system | A reference frame with axes used to describe the position and direction of forces, often aligned with the direction of acceleration to simplify analysis. |
| force | A vector quantity that describes the interaction between two objects or systems. |
| free-body diagram | A visual representation showing all forces exerted on an object or system, with each force drawn as a vector originating from the center of mass. |
| interaction | The mutual influence or action between two objects or systems that results in forces. |
| net force | The vector sum of all forces acting on an object or system. |
| vector | A quantity that has both magnitude and direction, used to represent forces on a free-body diagram. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces. |
| ideal pulley | A theoretical pulley with negligible mass that rotates about its center of mass with negligible friction. |
| ideal string | A theoretical string with negligible mass that does not stretch when under tension. |
| internal forces | Forces that objects within a system exert on each other, which do not affect the motion of the system's center of mass. |
| Newton's third law | The principle that when one object exerts a force on another object, the second object exerts an equal and opposite force on the first object. |
| paired forces | Two equal and opposite forces that act on different objects as a result of their interaction, as described by Newton's third law. |
| tension | The macroscopic net force that segments of a string, cable, chain, or similar system exert on each other in response to an external force. |
| Term | Definition |
|---|---|
| balanced forces | Forces acting on a system such that their vector sum equals zero in a particular dimension. |
| inertial reference frame | A reference frame in which Newton's laws of motion are valid; a frame that is either at rest or moving at constant velocity. |
| net force | The vector sum of all forces acting on an object or system. |
| translational equilibrium | The configuration of forces such that the net force exerted on a system is zero, resulting in constant velocity. |
| unbalanced forces | Forces acting on a system such that their vector sum is not zero, resulting in acceleration in that direction. |
| vector sum | The result of adding two or more vectors by combining their components. |
| velocity | A vector quantity that describes the rate of change of an object's position with respect to time. |
| Term | Definition |
|---|---|
| acceleration | A vector quantity that describes the rate of change of an object's velocity with respect to time. |
| center of mass | The point in a system where the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces. |
| net external force | The vector sum of all external forces acting on an object or system, which determines the rate of change of the system's momentum. |
| net force | The vector sum of all forces acting on an object or system. |
| Newton's second law of motion | The principle that the net force on an object equals the rate of change of its momentum, expressed as Fnet = dp/dt = ma. |
| system | A defined collection of objects whose energy and interactions are being analyzed. |
| unbalanced forces | Forces acting on a system such that their vector sum is not zero, resulting in acceleration in that direction. |
| velocity | A vector quantity that describes the rate of change of an object's position with respect to time. |
| Term | Definition |
|---|---|
| accelerating | Changing velocity; experiencing a net force that causes a change in speed or direction of motion. |
| apparent weight | The magnitude of the normal force exerted on a system; the weight that a system appears to have based on the support force acting on it. |
| center of mass | The point in a system where the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces. |
| differential mass | An infinitesimally small element of mass, denoted as dm, used in integration to calculate properties of nonuniform solids. |
| equivalence of inertial and gravitational mass | The experimentally verified principle that an object's inertial mass and gravitational mass are equal. |
| equivalence principle | The principle stating that an observer in a noninertial reference frame cannot distinguish between the effects of acceleration and the effects of a gravitational field. |
| gravitational field | The region of space around a mass where gravitational force is exerted on other masses; its strength is measured in N/kg. |
| gravitational field strength | The magnitude of the gravitational field at a point in space, equal to the gravitational force per unit mass, measured in N/kg or m/s². |
| gravitational force | The attractive force between two objects due to their masses, described by Newton's law of universal gravitation. |
| gravitational interaction | The attractive force exerted between two objects or systems due to their masses. |
| gravitational mass | A property of an object that relates to the force of attraction between two systems with mass. |
| inertia | The property of an object that resists changes in its motion. |
| inertial mass | A property of an object that determines how much its motion resists changes when interacting with another object; a measure of an object's inertia. |
| Newton's law of universal gravitation | The law stating that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. |
| Newton's shell theorem | A principle stating that the gravitational force exerted by a uniform spherical shell depends on whether an object is inside or outside the shell. |
| noninertial reference frame | A reference frame that is accelerating or rotating, in which Newton's laws do not hold without introducing fictitious forces. |
| normal force | The contact force exerted by a surface on an object perpendicular to that surface. |
| partial mass | The portion of a sphere's mass located within a distance from the center equal to or less than an object's distance from the center. |
| spherical shell | A thin, hollow sphere with mass distributed uniformly over its surface. |
| test object | A small object of known mass used to measure the gravitational field strength created by another mass. |
| uniform density | A property of an object where mass is distributed evenly throughout its volume, resulting in constant mass per unit volume. |
| uniform spherical distribution of mass | A sphere with mass distributed evenly throughout its volume, with constant density. |
| weight | The gravitational force exerted by an astronomical body on a relatively small nearby object. |
| weightless | The condition in which a system experiences no apparent weight, occurring when no forces act on the system or when gravity is the only force acting on it. |
| Term | Definition |
|---|---|
| coefficient of kinetic friction | A dimensionless constant (μₖ) that represents the ratio of kinetic friction force to the normal force between two surfaces that are sliding relative to each other. |
| coefficient of static friction | A dimensionless constant (μₛ) that represents the ratio of the maximum static friction force to the normal force between two surfaces. |
| friction | A nonconservative force that opposes motion and dissipates mechanical energy. |
| kinetic friction | The friction force exerted on a system moving relative to a surface, which acts at the point of contact and dissipates energy. |
| material properties | The characteristics of materials that affect how they interact, such as surface texture and composition, which determine the coefficient of kinetic friction. |
| normal force | The contact force exerted by a surface on an object perpendicular to that surface. |
| relative motion | The motion of one surface with respect to another surface in contact with it. |
| slipping | A situation in which two surfaces in contact are moving relative to each other. |
| static friction | A friction force that acts between two surfaces in contact that are not moving relative to each other, preventing an object from slipping or sliding. |
| Term | Definition |
|---|---|
| equilibrium position | The position where the spring force on an object is zero and the object-spring system is at rest. |
| equivalent spring constant | A single spring constant that represents the combined effect of multiple springs exerting forces on an object. |
| Hooke's law | The principle that the force exerted by an ideal spring is proportional to its displacement from equilibrium, expressed as F_s = -kΔx. |
| ideal spring | A theoretical spring that obeys Hooke's law and stores elastic potential energy proportional to the square of its displacement. |
| nonideal spring | A spring that either has nonnegligible mass or exerts a force that is not proportional to its change in length from its relaxed length. |
| relaxed length | The natural length of a spring when no external force is applied to it. |
| spring constant | A measure of a spring's stiffness, represented by k, that relates the force exerted by the spring to its displacement from equilibrium. |
| springs in parallel | An arrangement of springs connected side-by-side, where each spring experiences the same displacement and forces add together. |
| springs in series | An arrangement of springs connected end-to-end, where the same force is transmitted through each spring and displacements add together. |
| Term | Definition |
|---|---|
| asymptote | A line or value that a function approaches but never reaches, determined by initial conditions and forces in resistive force problems. |
| differential equation | An equation relating a function to its derivatives, used to describe how velocity changes with time under a resistive force. |
| exponential function | A mathematical function describing position, velocity, and acceleration of an object under a resistive force, characterized by constant percentage change over time. |
| initial conditions | The starting values of position, velocity, and acceleration used to determine the specific motion of an object under a resistive force. |
| net force | The vector sum of all forces acting on an object or system. |
| resistive force | A velocity-dependent force that acts in the opposite direction of an object's velocity, opposing its motion. |
| separation of variables | A mathematical method for solving differential equations by rearranging terms so that each variable appears on only one side of the equation. |
| terminal velocity | The maximum constant speed achieved by an object when the net force acting on it becomes zero, occurring when the resistive force balances other forces. |
| velocity-dependent force | A force whose magnitude depends on the velocity of an object, typically proportional to velocity or velocity squared. |