| Term | Definition |
|---|---|
| angular velocity | The rate of change of angular position with respect to time, represented by the symbol ω. |
| 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. |
| 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. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| rotational inertia | A measure of an object's resistance to changes in its rotational motion about a given axis; depends on both the mass of the object and how that mass is distributed relative to the axis of rotation. |
| rotational kinetic energy | The kinetic energy of a rigid system due to its rotation about an axis, calculated as half the product of rotational inertia and the square of angular velocity. |
| scalar | A physical quantity that has only magnitude and no direction. |
| Term | Definition |
|---|---|
| angular displacement | The change in angular position of a rotating object, measured in radians. |
| energy transfer | The process by which energy moves into or out of a system through the action of forces or torques. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| torque | A measure of the rotational effect of a force on a rigid body, calculated as the product of the force component perpendicular to the position vector and the distance from the axis of rotation. |
| work | Energy transferred to or from a system by forces or torques acting on it. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time, represented by the symbol α. |
| angular impulse | The product of net torque and the time interval over which it acts, equal to the change in angular momentum of an object or system. |
| 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 cross product of position vector and linear momentum. |
| angular velocity | The rate of change of angular position with respect to time, represented by the symbol ω. |
| impulse-momentum theorem | The relationship stating that the impulse exerted on an object equals its change in momentum. |
| moment of inertia | A measure of a rigid body's resistance to rotational acceleration about a given axis, represented by the symbol I. |
| momentum | A vector quantity defined as the product of an object's mass and velocity (p=mv), used to describe the motion of objects and systems. |
| Newton's second law | The principle that the net force on an object equals the product of its mass and acceleration; in rotational form, net torque equals rotational inertia times angular acceleration. |
| radial distance | The perpendicular distance from a reference point or axis to an object's position. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| rotational inertia | A measure of an object's resistance to changes in its rotational motion about a given axis; depends on both the mass of the object 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 body, calculated as the product of the force component perpendicular to the position vector and the distance from the axis of rotation. |
| Term | Definition |
|---|---|
| angular impulse | The product of net torque and the time interval over which it acts, equal to the change in angular momentum of an object or system. |
| 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 cross product of position vector and linear momentum. |
| angular speed | The rate at which an object rotates about a rotational axis, measured in radians per unit time. |
| conservation of angular momentum | The principle that the total angular momentum of a system remains constant when the net external torque on the system is zero. |
| net external torque | The total rotational force applied to a system from outside its boundaries. |
| nonrigid system | A system whose shape or configuration can change, allowing mass to move closer to or farther from the rotational axis. |
| rotational axis | The fixed line or point about which a system rotates or is analyzed for angular motion. |
| system | A defined collection of objects whose energy and interactions are being analyzed. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time, represented by the symbol α. |
| angular displacement | The change in angular position of a rotating object, measured in radians. |
| angular velocity | The rate of change of angular position with respect to time, represented by the symbol ω. |
| 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. |
| energy dissipation | The process by which mechanical energy is lost from a system, in this case due to the work done by kinetic friction during slipping. |
| frictional force | The force that acts at the contact point between a rolling object and a surface; in ideal rolling without slipping, it does not dissipate energy from the system. |
| 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 exerted on a system moving relative to a surface, which acts at the point of contact and dissipates energy. |
| rolling while slipping | Motion of a system where the center of mass translation and rotational motion are not directly related due to slipping relative to a surface. |
| rolling without slipping | A motion condition where a rolling object's translational and rotational motions are related such that the contact point with the surface has zero velocity, with no relative sliding between the object and surface. |
| rotational kinetic energy | The kinetic energy of a rigid system due to its rotation about an axis, calculated as half the product of rotational inertia and the square of angular velocity. |
| rotational motion | The motion of a rigid body or point rotating about a fixed axis, characterized by angular displacement, velocity, and acceleration. |
| slipping | A situation in which two surfaces in contact are moving relative to each other. |
| translational motion | The motion of an object's center of mass moving from one location to another through space. |
| 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 cross product of position vector and linear momentum. |
| 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. |
| conservation of energy | The principle that total mechanical energy remains constant in an isolated gravitational system. |
| elliptical orbit | An orbital path where a satellite's distance from the central object varies, resulting in changing speed and kinetic energy while maintaining constant total energy. |
| escape velocity | The minimum velocity required for a satellite to escape the gravitational pull of a central object, at which the total mechanical energy equals zero. |
| gravitational force | The attractive force between two objects due to their masses, described by Newton's law of universal gravitation. |
| gravitational potential energy | The energy stored in a system due to the gravitational interaction between a satellite and a central object, defined as zero at infinite 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 an orbiting system, which remains constant in both circular and elliptical orbits. |