| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| direction | The orientation or path along which a quantity is measured, which depends on the choice of reference frame. |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| distance | A scalar quantity representing the total length of the path traveled by an object. |
| magnitude | The size or amount of a measured quantity, which can vary depending on the observer's reference frame. |
| one-dimensional coordinate system | A reference system used to describe positions and directions along a single axis, typically represented as a number line. |
| opposite directions | Directions that are 180 degrees apart on a coordinate system, represented by opposite signs in one-dimensional calculations. |
| position | A vector quantity describing the location of an object relative to a reference point. |
| scalar | A physical quantity that has magnitude only, without direction. |
| speed | A scalar quantity representing the rate at which an object covers distance. |
| vector | A quantity that has both magnitude and direction, which can be represented as the sum of perpendicular components. |
| vector component | The projection of a vector along a specific axis or direction, which in one dimension is indicated by the sign of the value. |
| vector sum | The result of adding two or more vectors together, taking into account both magnitude and direction. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| average acceleration | The change in velocity of an object divided by the time interval over which that change occurs. |
| average velocity | The displacement of an object divided by the time interval over which that displacement occurs. |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| instantaneous acceleration | The acceleration of an object at a specific instant in time, equal to the slope of the tangent line to a velocity-time graph. |
| instantaneous velocity | The velocity of an object at a specific instant in time, equal to the slope of the tangent line to a position-time graph. |
| object model | A simplification in physics where an object is treated as a single point with properties like mass and charge, ignoring size, shape, and internal structure. |
| position | A vector quantity describing the location of an object relative to a reference point. |
| time interval | The duration of time over which a change in an object's motion is measured. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| constant acceleration | Motion in which an object's acceleration remains the same throughout the time interval being analyzed. |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| gravitational acceleration | The constant downward acceleration of objects near Earth's surface due to gravity, approximately 10 m/s². |
| instantaneous acceleration | The acceleration of an object at a specific instant in time, equal to the slope of the tangent line to a velocity-time graph. |
| instantaneous velocity | The velocity of an object at a specific instant in time, equal to the slope of the tangent line to a position-time graph. |
| kinematic equations | Mathematical equations used to describe the motion of an object under constant acceleration in one dimension. |
| motion diagrams | Visual representations of an object's motion showing its position at successive time intervals. |
| position | A vector quantity describing the location of an object relative to a reference point. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| coordinate system | A reference framework used to resolve vectors into their perpendicular components, typically using horizontal and vertical axes. |
| direction | The orientation or path along which a quantity is measured, which depends on the choice of reference frame. |
| inertial reference frame | A reference frame in which Newton's laws of motion apply; a frame that is either at rest or moving at constant velocity. |
| magnitude | The size or amount of a measured quantity, which can vary depending on the observer's reference frame. |
| observed velocity | The velocity of an object as measured by an observer in a particular reference frame, determined by combining the object's velocity with the observer's frame velocity. |
| observer | A person or point of view from which physical phenomena are measured and described. |
| vector addition | The mathematical process of combining two or more vectors to find a resultant vector, used when combining velocities from different reference frames. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| coordinate system | A reference framework used to resolve vectors into their perpendicular components, typically using horizontal and vertical axes. |
| kinematic relationships | Mathematical equations that describe the motion of objects in terms of displacement, velocity, acceleration, and time. |
| motion components | The separation of two-dimensional motion into independent one-dimensional motions along perpendicular axes. |
| perpendicular components | The parts of a vector that are at right angles to each other, obtained by breaking down a vector into horizontal and vertical parts. |
| projectile motion | A special case of two-dimensional motion in which an object experiences zero acceleration in one dimension and constant, nonzero acceleration in the perpendicular dimension. |
| resultant | The single vector that represents the combined effect of two or more perpendicular component vectors. |
| trigonometric functions | Mathematical functions (sine, cosine, tangent) used to calculate the perpendicular components of a vector based on its magnitude and angle. |
| two-dimensional motion | Motion of an object that occurs in two perpendicular directions simultaneously. |
| vector | A quantity that has both magnitude and direction, which can be represented as the sum of perpendicular components. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| constituent objects | The individual objects that make up a system. |
| constituent parts | The individual objects or components that make up a larger system. |
| energy transfer | The movement of energy from one part of a system to another or between a system and its environment. |
| 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 is evenly distributed, 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, rather than at the atomic or molecular level. |
| mass transfer | The movement of matter from one part of a system to another or between a system and its environment. |
| symmetrical mass distribution | An arrangement of mass in a system where the mass is evenly distributed about one or more lines or planes of symmetry. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| system properties | The characteristics and behaviors of a system that are determined by the interactions between objects within it. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose 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 framework used to resolve vectors into their perpendicular components, typically using horizontal and vertical axes. |
| force | A vector quantity that describes the interaction between two objects or systems. |
| free-body diagram | A visual representation that shows all forces exerted on an object or system, with each force drawn as a vector originating from the object's center of mass. |
| interaction | The mutual influence or effect between two objects or systems, which produces a force. |
| interatomic electric forces | The electromagnetic forces between atoms that produce the macroscopic effects observed as contact forces. |
| net force | The vector sum of all forces acting on an object or system. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| vector | A quantity that has both magnitude and direction, which can be represented as the sum of perpendicular components. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose 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 under tension and has uniform tension throughout its length. |
| 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 forces always occur in equal and opposite pairs: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. |
| paired forces | Two equal and opposite forces that result from the interaction between two objects, 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 that result in a net force of zero in a particular dimension. |
| inertial reference frame | A reference frame in which Newton's laws of motion apply; 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. |
| Newton's first law | The principle stating that if the net force exerted on a system is zero, the velocity of that system will remain constant. |
| translational equilibrium | A state in which an object's linear velocity remains constant because the net force exerted on it is zero. |
| unbalanced forces | A configuration of forces where the net force exerted on a system is not equal to zero, resulting in acceleration. |
| vector sum | The result of adding two or more vectors together, taking into account both magnitude and direction. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| net force | The vector sum of all forces acting on an object or system. |
| Newton's second law of motion | The principle stating that the acceleration of a system's center of mass is proportional to the net force exerted on it and occurs in the same direction as that force. |
| nonzero net external force | A net force applied to a system from outside that is not equal to zero, causing the system's velocity to change. |
| unbalanced forces | A configuration of forces where the net force exerted on a system is not equal to zero, resulting in acceleration. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| 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 moving 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 that acts between two surfaces when they are in contact and moving relative to each other. |
| normal force | The perpendicular component of the force exerted on an object by a surface, directed away from the surface. |
| 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 |
|---|---|
| banked surface | An inclined surface on which an object travels in a circular path, where normal force and friction components contribute to centripetal acceleration. |
| centripetal acceleration | The component of an object's acceleration directed toward the center of its circular path. |
| 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. |
| circular path | The trajectory followed by an object moving in a circle around a fixed center point. |
| conical pendulum | A pendulum that moves in a horizontal circle, 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, typically measured in hertz (Hz). |
| gravitational attraction | The force of gravity exerted by a central body on a satellite, which provides the centripetal force necessary for circular orbital motion. |
| gravitational force | The attractive force due to mass, which can serve as the sole source of centripetal acceleration at the top of a vertical circular loop. |
| Kepler's third law | A principle 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 centripetal acceleration and tangential acceleration for an object moving in a circle. |
| normal force | The perpendicular component of the force exerted on an object by a surface, directed away from the surface. |
| orbital period | The time it takes for a satellite to complete one full orbit around a central body. |
| orbital radius | The distance from the center of a central body to a satellite in 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 traveling on 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 component of linear acceleration directed along the tangent to the circular path of a rotating point, related to angular acceleration by a_T = rα. |
| 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 |
|---|---|
| coordinate system | A reference framework used to resolve vectors into their perpendicular components, typically using horizontal and vertical axes. |
| scalar | A physical quantity that has magnitude only, without direction. |
| translational kinetic energy | The kinetic energy associated with the linear motion of an object's center of mass. |
| Term | Definition |
|---|---|
| air resistance | A nonconservative force exerted by air on a moving object that opposes its motion. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| conservative forces | Forces for which the work done is independent of the path taken, and energy can be stored as potential energy (such as gravitational or elastic forces). |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| friction | A nonconservative force that opposes motion and dissipates mechanical energy. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| mechanical energy | The sum of a system's kinetic and potential energies. |
| net work | The sum of all work done by all forces exerted on an object. |
| nonconservative force | A force for which the work done is path-dependent, such as friction or air resistance. |
| potential energy | The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces. |
| scalar | A physical quantity that has magnitude only, without direction. |
| work | The amount of energy transferred into or out of a system by a force exerted on that system over a distance. |
| work-energy theorem | The principle stating that the change in an object's kinetic energy equals the net work done by all forces exerted on the object. |
| Term | Definition |
|---|---|
| conservative forces | Forces for which the work done is independent of the path taken, and energy can be stored as potential energy (such as gravitational or elastic forces). |
| elastic potential energy | The potential energy stored in a spring or elastic object due to its deformation from equilibrium length. |
| equilibrium length | The natural length of a spring when no external forces are applied to stretch or compress it. |
| gravitational field | The region of space around a mass where gravitational force is exerted on other masses. |
| gravitational potential energy | The potential energy of a system due to the gravitational interaction between two masses separated by a distance. |
| ideal spring | A theoretical spring that obeys Hooke's law and stores elastic potential energy proportional to the square of its displacement. |
| potential energy | The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces. |
| scalar | A physical quantity that has magnitude only, without direction. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| zero potential energy | A reference point chosen by an observer to simplify analysis of a system's potential energy. |
| Term | Definition |
|---|---|
| conservation of mechanical energy | The principle that the total mechanical energy of a system remains constant when only conservative forces act on it, or changes by an amount equal to energy transferred into or out of the system. |
| conservative forces | Forces for which the work done is independent of the path taken, and energy can be stored as potential energy (such as gravitational or elastic forces). |
| energy | The capacity to do work or cause change; a conserved quantity that can be transferred between a system and its environment. |
| energy transfer | The movement of energy from one part of a system to another or between a system and its environment. |
| environment | Everything outside the defined system; the region with which the system can exchange energy through work or other interactions. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| mechanical energy | The sum of a system's kinetic and potential energies. |
| nonconservative interactions | Interactions within a system, such as friction or air resistance, that dissipate mechanical energy and cause the total mechanical energy to decrease. |
| potential energy | The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| work | The amount of energy transferred into or out of a system by a force exerted on that system over a distance. |
| Term | Definition |
|---|---|
| average power | The total amount of energy transferred or converted divided by the time interval over which the transfer or conversion occurs. |
| energy transfer | The movement of energy from one part of a system to another or between a system and its environment. |
| instantaneous power | The rate of energy transfer at a specific moment in time, calculated as the component of force parallel to velocity multiplied by that velocity. |
| power | The rate at which energy is transferred into, out of, or converted within a system with respect to time. |
| work | The amount of energy transferred into or out of a system by a force exerted on that system over a distance. |
| Term | Definition |
|---|---|
| collision | An interaction between objects where the forces exerted between them are much larger than external forces, allowing analysis of initial and final states. |
| explosion | An interaction in which internal forces within a system move objects apart. |
| momentum | A vector quantity that describes the motion of an object, equal to mass times velocity, with direction matching the velocity. |
| object model | A simplification in physics where an object is treated as a single point with properties like mass and charge, ignoring size, shape, and internal structure. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| vector | A quantity that has both magnitude and direction, which can be represented as the sum of perpendicular components. |
| Term | Definition |
|---|---|
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| center-of-mass velocity | The velocity of the center of mass of a system, calculated as the total momentum divided by the total mass. |
| collision | An interaction between objects where the forces exerted between them are much larger than external forces, allowing analysis of initial and final states. |
| conservation of momentum | The principle that the total momentum of a system remains constant when no net external force acts on the system. |
| explosion | An interaction in which internal forces within a system move objects apart. |
| impulse | The change in momentum of an object, equal to the force applied multiplied by the time interval over which it acts. |
| momentum | A vector quantity that describes the motion of an object, equal to mass times velocity, with direction matching the velocity. |
| net external force | The vector sum of all forces acting on a system from outside the system. |
| Newton's third law | The principle that forces always occur in equal and opposite pairs: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| Term | Definition |
|---|---|
| elastic collision | A collision between objects in which the total kinetic energy of the system is conserved, remaining equal before and after the collision. |
| inelastic collision | A collision between objects in which the total kinetic energy of the system decreases, with some kinetic energy transformed into other forms of energy by nonconservative forces. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| nonconservative force | A force for which the work done is path-dependent, such as friction or air resistance. |
| perfectly inelastic collision | A collision in which the colliding objects stick together and move with the same velocity after the collision. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time. |
| angular displacement | The measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. |
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| axis of rotation | The fixed line about which a system rotates. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| constant angular acceleration | A situation in which angular velocity changes at a uniform rate over time. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time. |
| angular displacement | The measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. |
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| axis of rotation | The fixed line about which a system rotates. |
| linear motion | Motion along a straight path, characterized by displacement, velocity, and acceleration in one dimension. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational motion | Motion of an object or system rotating about a fixed axis, characterized by angular displacement, angular velocity, and angular acceleration. |
| tangential acceleration | The component of linear acceleration directed along the tangent to the circular path of a rotating point, related to angular acceleration by a_T = rα. |
| tangential velocity | The linear velocity of a point on a rotating system directed along the tangent to its circular path, related to angular velocity by v = rω. |
| Term | Definition |
|---|---|
| axis of rotation | The fixed line about which a system rotates. |
| force component perpendicular | The portion of an applied force that acts at a right angle to the position vector from the axis of rotation. |
| force diagram | A diagram used to represent and analyze the forces and torques exerted on a rigid system, showing the magnitude, direction, and point of application of each force relative to the axis of rotation. |
| free-body diagram | A visual representation that shows all forces exerted on an object or system, with each force drawn as a vector originating from the object's center of mass. |
| lever arm | The perpendicular distance from the axis of rotation to the line of action of an applied force. |
| line of action | The straight line along which a force acts, extending infinitely in both directions. |
| perpendicular force | The component of a force that is perpendicular to the position vector, which directly contributes to torque production. |
| position vector | A vector drawn from the axis of rotation to the point where a force is applied on a rigid system. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| torque | A measure of the rotational effect of a force on a rigid system, calculated as the product of the force and its perpendicular distance from the axis of rotation. |
| Term | Definition |
|---|---|
| axis of rotation | The fixed line about which a system rotates. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| mass distribution | The spatial arrangement of mass within a system relative to a reference point or axis, which affects the system's rotational inertia. |
| parallel axis theorem | A theorem that relates the rotational inertia of a rigid system about any axis parallel to an axis through its center of mass, expressed as I' = I_cm + Md². |
| perpendicular distance | The shortest distance from a point or object to the axis of rotation, measured at a right angle to the axis. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational inertia | A measure of a rigid system's resistance to changes in its rotational motion, dependent on both the mass of the system and how that mass is distributed relative to the axis of rotation. |
| Term | Definition |
|---|---|
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| force diagram | A diagram used to represent and analyze the forces and torques exerted on a rigid system, showing the magnitude, direction, and point of application of each force relative to the axis of rotation. |
| free-body diagram | A visual representation that shows all forces exerted on an object or system, with each force drawn as a vector originating from the object's center of mass. |
| net torque | The sum of all torques acting on an object or system, which determines whether angular velocity will change. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational equilibrium | A state in which a system maintains constant angular velocity because the net torque exerted on it is zero. |
| torque | A measure of the rotational effect of a force on a rigid system, calculated as the product of the force and its perpendicular distance from the axis of rotation. |
| translational equilibrium | A state in which an object's linear velocity remains constant because the net force exerted on it is zero. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time. |
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| net torque | The sum of all torques acting on an object or system, which determines whether angular velocity will change. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational inertia | A measure of a rigid system's resistance to changes in its rotational motion, dependent on both the mass of the system and how that mass is distributed relative to the axis of rotation. |
| Term | Definition |
|---|---|
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational inertia | A measure of a rigid system's resistance to changes in its rotational motion, dependent on both the mass of the system and how that mass is distributed relative to the axis of rotation. |
| rotational kinetic energy | The kinetic energy possessed by a rigid system due to its rotation about an axis, calculated as K = 1/2 I ω². |
| scalar | A physical quantity that has magnitude only, without direction. |
| translational kinetic energy | The kinetic energy associated with the linear motion of an object's center of mass. |
| Term | Definition |
|---|---|
| angular displacement | The measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. |
| angular position | The rotational location of an object, typically measured as an angle from a reference direction. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| torque | A measure of the rotational effect of a force on a rigid system, calculated as the product of the force and its perpendicular distance from the axis of rotation. |
| work | The amount of energy transferred into or out of a system by a force exerted on that system over a distance. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time. |
| angular impulse | The product of the torque exerted on an object or rigid system and the time interval during which the torque is exerted, calculated as τΔt. |
| angular momentum | A measure of the rotational motion of an object or system, calculated as the product of moment of inertia and angular velocity, or as the product of mass, velocity, and perpendicular distance from a reference point. |
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| impulse-momentum theorem | A principle relating the impulse applied to an object to its change in momentum; in rotational form, it relates angular impulse to change in angular momentum. |
| Newton's second law of motion | The principle stating that the acceleration of a system's center of mass is proportional to the net force exerted on it and occurs in the same direction as that force. |
| radial distance | The perpendicular distance from a reference point or axis to an object. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| rotational inertia | A measure of a rigid system's resistance to changes in its rotational motion, dependent on both the mass of the system and how that mass is distributed relative to the axis of rotation. |
| torque | A measure of the rotational effect of a force on a rigid system, calculated as the product of the force and its perpendicular distance from the axis of rotation. |
| Term | Definition |
|---|---|
| angular impulse | The product of the torque exerted on an object or rigid system and the time interval during which the torque is exerted, calculated as τΔt. |
| angular momentum | A measure of the rotational motion of an object or system, calculated as the product of moment of inertia and angular velocity, or as the product of mass, velocity, and perpendicular distance from a reference point. |
| angular momentum transfer | The process by which angular momentum is exchanged between a system and its environment when net external torque is nonzero. |
| angular speed | The rate at which an object or system rotates about a rotational axis, measured in radians per unit time. |
| axis of rotation | The fixed line about which a system rotates. |
| conservation of angular momentum | The principle that the total angular momentum of a system remains constant when the net external torque is zero. |
| net external torque | The total rotational force applied to a system from outside sources. |
| nonrigid system | A system whose shape or configuration can change, allowing mass to move closer to or further from the rotational axis. |
| rigid system | A system that holds its shape but in which different points on the system move in different directions during rotation. |
| system | A collection of objects and their interactions that are studied together as a single unit. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time. |
| angular displacement | The measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. |
| angular velocity | The rate at which an object or system rotates, measured as the change in angular position per unit time. |
| center of mass | The point in a system where all the mass can be considered to be concentrated for the purpose of analyzing motion and forces. |
| energy dissipation | The process by which mechanical energy is converted to other forms (such as heat) and removed from a system. |
| friction | A nonconservative force that opposes motion and dissipates mechanical energy. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| kinetic friction | The friction force that acts between two surfaces when they are in contact and moving relative to each other. |
| rolling | Motion of a system that combines both translational motion of its center of mass and rotational motion about its center of mass. |
| rolling without slipping | Motion of a rolling object where the contact point with the surface has zero velocity, meaning the translational and rotational motions are related by the constraint that the distance traveled by the center of mass equals the arc length rotated. |
| rotational kinetic energy | The kinetic energy possessed by a rigid system due to its rotation about an axis, calculated as K = 1/2 I ω². |
| rotational motion | Motion of an object or system rotating about a fixed axis, characterized by angular displacement, angular velocity, and angular acceleration. |
| slipping | A situation in which two surfaces in contact are moving relative to each other. |
| translational kinetic energy | The kinetic energy associated with the linear motion of an object's center of mass. |
| translational motion | Motion of an object's center of mass through space, described by the displacement, velocity, and acceleration of the center of mass. |
| Term | Definition |
|---|---|
| angular momentum | A measure of the rotational motion of an object or system, calculated as the product of moment of inertia and angular velocity, or as the product of mass, velocity, and perpendicular distance from a reference point. |
| circular orbits | Orbital paths where a satellite maintains a constant distance from the central object, resulting in constant speed and energy. |
| conservation laws | Physical principles stating that certain quantities (such as energy and angular momentum) remain constant in an isolated system. |
| elliptical orbits | Orbital paths where a satellite's distance from the central object varies, causing changes in speed and kinetic energy while total mechanical energy remains constant. |
| escape velocity | The minimum velocity required for a satellite to escape the gravitational pull of a central object, achieved when the system's total mechanical energy equals zero. |
| gravitational force | The attractive force due to mass, which can serve as the sole source of centripetal acceleration at the top of a vertical circular loop. |
| gravitational potential energy | The potential energy of a system due to the gravitational interaction between two masses separated by a distance. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| total mechanical energy | The sum of kinetic and potential energy in a system; remains constant in both circular and elliptical orbits. |
| Term | Definition |
|---|---|
| angular displacement | The measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| equilibrium position | The central position around which an object oscillates in SHM, where the net force is zero. |
| periodic motion | Motion that repeats at regular time intervals. |
| restoring force | A force exerted on an object in a direction opposite to its displacement from an equilibrium position, acting to return the object to equilibrium. |
| restoring torque | A rotational force that acts in a direction opposite to angular displacement, returning an object toward its equilibrium orientation. |
| simple harmonic motion | A special case of periodic motion in which a restoring force proportional to displacement causes an object to oscillate about an equilibrium position. |
| Term | Definition |
|---|---|
| frequency | The number of complete oscillations or cycles of simple harmonic motion that occur per unit time, typically measured in hertz (Hz). |
| object-ideal-spring oscillator | A system consisting of a mass attached to an ideal spring that undergoes simple harmonic motion. |
| period | The time required for an object to complete one full circular path, rotation, or cycle. |
| simple harmonic motion | A special case of periodic motion in which a restoring force proportional to displacement causes an object to oscillate about an equilibrium position. |
| simple pendulum | A mass suspended from a fixed point by a string or rod of negligible mass that swings back and forth in simple harmonic motion. |
| Term | Definition |
|---|---|
| acceleration | The rate of change of velocity with respect to time. |
| amplitude | The maximum displacement of an oscillating system from its equilibrium position; determines the maximum potential energy and total energy of the system. |
| displacement | A vector quantity representing the change in position of an object from its initial to final location. |
| equilibrium position | The central position around which an object oscillates in SHM, where the net force is zero. |
| extrema | The maximum or minimum values of displacement, velocity, or acceleration in SHM. |
| frequency | The number of complete oscillations or cycles of simple harmonic motion that occur per unit time, typically measured in hertz (Hz). |
| harmonic motion | Repetitive motion characterized by displacement, velocity, and acceleration that vary periodically with time. |
| period | The time required for an object to complete one full circular path, rotation, or cycle. |
| velocity | A vector quantity that describes both the speed and direction of an object's motion. |
| Term | Definition |
|---|---|
| amplitude | The maximum displacement of an oscillating system from its equilibrium position; determines the maximum potential energy and total energy of the system. |
| conservation of energy | The principle that the total mechanical energy of a system remains constant when only conservative forces act on it. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| mechanical energy | The sum of a system's kinetic and potential energies. |
| potential energy | The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces. |
| simple harmonic motion | A special case of periodic motion in which a restoring force proportional to displacement causes an object to oscillate about an equilibrium position. |
| total mechanical energy | The sum of kinetic and potential energy in a system; remains constant in both circular and elliptical orbits. |
| Term | Definition |
|---|---|
| density | A measure of how much mass is contained in a given volume of a substance, calculated as the ratio of mass to volume. |
| fluid | A substance that can flow and conform to the shape of its container, including liquids and gases. |
| gas | A state of matter with no fixed shape or volume, where atoms and molecules have minimal interactions and move freely. |
| ideal fluid | A theoretical fluid that is incompressible and has no viscosity, used as a model for analyzing fluid behavior. |
| incompressible | A property of a fluid that cannot be reduced in volume by the application of pressure. |
| liquid | A state of matter with a fixed volume but no fixed shape, where atoms and molecules have moderate interactions. |
| mass | The amount of matter in an object, typically measured in kilograms. |
| solid | A state of matter with a fixed shape and fixed volume, where atoms and molecules are tightly bonded. |
| viscosity | A measure of a fluid's resistance to flow, or its internal friction. |
| volume | The amount of space occupied by a substance or object, typically measured in cubic meters or liters. |
| Term | Definition |
|---|---|
| absolute pressure | The total pressure at a given point in a fluid, equal to the sum of a reference pressure and the gauge pressure. |
| atmospheric pressure | The pressure exerted by the weight of the atmosphere, commonly used as a reference pressure (Patm). |
| fluid | A substance that can flow and conform to the shape of its container, including liquids and gases. |
| gauge pressure | The pressure of a fluid measured relative to a reference pressure, typically atmospheric pressure, calculated as the difference between absolute pressure and reference pressure. |
| incompressible fluid | A fluid whose density remains essentially constant during flow, regardless of pressure changes. |
| perpendicular force component | The component of a force that acts at a right angle to a surface. |
| pressure | The magnitude of the perpendicular force component exerted per unit area over a given surface area. |
| reference pressure | A baseline pressure used as a starting point for measuring gauge pressure, such as atmospheric pressure (P0). |
| scalar | A physical quantity that has magnitude only, without direction. |
| Term | Definition |
|---|---|
| buoyant force | The net upward force exerted on an object by a fluid as a result of pressure differences across the object's surface. |
| constituent particles | The individual molecules or atoms that make up a fluid. |
| external forces | Forces applied to a fluid from outside sources that affect its motion and behavior. |
| fluid | A substance that can flow and conform to the shape of its container, including liquids and gases. |
| fluid displaced | The volume of fluid that is pushed aside or occupies the space taken up by a submerged or partially submerged object. |
| fluid velocity | The speed and direction of fluid motion, which changes in response to internal particle interactions and external forces. |
| internal interactions | The forces and interactions between particles within a fluid that contribute to its macroscopic behavior. |
| macroscopic behavior | The large-scale, observable behavior of a fluid as a whole, resulting from the combined effects of internal particle interactions and external forces. |
| Newton's laws | The three fundamental laws of motion that describe how forces affect the motion of objects, including particles within a fluid. |
| weight of fluid displaced | The gravitational force exerted on the volume of fluid that an object displaces, which equals the magnitude of the buoyant force. |
| Term | Definition |
|---|---|
| Bernoulli's equation | A mathematical equation describing the conservation of mechanical energy in fluid flow, relating pressure, gravitational potential energy, and kinetic energy at two points in a fluid. |
| conservation of mechanical energy | The principle that the total mechanical energy of a system remains constant when only conservative forces act on it, or changes by an amount equal to energy transferred into or out of the system. |
| continuity equation | The mathematical relationship stating that the mass flow rate of an incompressible fluid remains constant throughout a tube, expressed as A₁v₁ = A₂v₂. |
| cross-sectional area | The area of a surface perpendicular to the direction of fluid flow through a tube or channel. |
| flow rate | The volume or mass of fluid passing through a cross-sectional area per unit time. |
| fluid flow | The motion of a fluid from one location to another, driven by differences in energy within the fluid-Earth system. |
| gravitational potential energy | The potential energy of a system due to the gravitational interaction between two masses separated by a distance. |
| incompressible fluid | A fluid whose density remains essentially constant during flow, regardless of pressure changes. |
| kinetic energy | The energy possessed by an object due to its motion, equal to one-half the product of its mass and the square of its velocity. |
| mass conservation | The principle that the total mass of a system remains constant over time, with no mass created or destroyed. |
| pressure | The magnitude of the perpendicular force component exerted per unit area over a given surface area. |
| pressure difference | The variation in pressure between two locations that causes a fluid to flow from higher to lower pressure. |
| Torricelli's theorem | A principle stating that the speed of a fluid exiting an opening is related to the vertical distance between the opening and the fluid's surface, derived from conservation of energy. |
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