| 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. |
| axis of rotation | The fixed line about which a rigid body or system rotates. |
| constant angular acceleration | A condition in which angular velocity changes at a uniform rate over time, allowing the use of kinematic equations to relate angular displacement, angular velocity, and angular acceleration. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| 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. |
| axis of rotation | The fixed line about which a rigid body or system rotates. |
| linear displacement | The linear distance s traveled by a point on a rotating system. |
| linear motion | The motion of a point along a straight or curved path, characterized by linear displacement, velocity, and acceleration. |
| linear velocity | The rate of change of linear displacement with respect to time, denoted by v, related to angular velocity by v = rω. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| rotational motion | The motion of a rigid body or point rotating about a fixed axis, characterized by angular displacement, velocity, and acceleration. |
| tangential acceleration | The rate at which an object's speed changes, directed tangent to the object's circular path. |
| Term | Definition |
|---|---|
| axis of rotation | The fixed line about which a rigid body or system rotates. |
| cross product | A vector operation between two vectors that produces a third vector perpendicular to both, with magnitude AB sin θ. |
| force component perpendicular | The component of a force that is perpendicular to the position vector, which is the only component that contributes to torque. |
| force diagram | A diagram that represents the forces exerted on an object or system. |
| 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. |
| lever arm | The perpendicular distance from the axis of rotation to the line of action of an applied force. |
| pivot point | The chosen point about which torque on a rigid system is calculated. |
| position vector | A vector denoted by r⃗ that specifies the location of a point relative to the origin. |
| right-hand rule | A method for determining the direction of a vector resulting from a cross product by orienting the fingers of the right hand in the direction of the first vector and curling them toward the second vector. |
| 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. |
| Term | Definition |
|---|---|
| axis of rotation | The fixed line about which a rigid body or system rotates. |
| 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. |
| mass distribution | The spatial arrangement of mass within a system relative to a reference point or axis. |
| parallel axis theorem | A theorem that relates the rotational inertia of a rigid system about any axis to its rotational inertia about a parallel axis through its center of mass, expressed as I' = I_cm + Md². |
| perpendicular distance | The shortest distance from a point or mass element to the axis of rotation, measured at a right angle to the axis. |
| 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. |
| Term | Definition |
|---|---|
| angular velocity | The rate of change of angular position with respect to time, represented by the symbol ω. |
| force diagram | A diagram that represents the forces exerted on an object or system. |
| 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. |
| net torque | The vector sum of all torques acting on an object or system, which causes changes in angular motion. |
| rigid system | A collection of objects or particles that maintain fixed distances from each other and rotate as a single unit. |
| 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 body, calculated as the product of the force component perpendicular to the position vector and the distance from the axis of rotation. |
| translational equilibrium | The configuration of forces such that the net force exerted on a system is zero, resulting in constant velocity. |
| Term | Definition |
|---|---|
| angular acceleration | The rate of change of angular velocity with respect to time, represented by the symbol α. |
| angular velocity | The rate of change of angular position with respect to time, represented by the symbol ω. |
| net torque | The vector sum of all torques acting on an object or system, which causes changes in angular motion. |
| 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. |