What is acceleration in AP Physics C: Mechanics?

A vector quantity that describes the rate of change of an object's velocity with respect to time.

What is component in AP Physics C: Mechanics?

The projection of a vector along a specific direction, such as the x-, y-, or z-direction.

What is direction in AP Physics C: Mechanics?

The orientation or path along which a vector quantity acts.

What is displacement in AP Physics C: Mechanics?

A vector quantity representing the change in position from an initial to a final location.

What is distance in AP Physics C: Mechanics?

A scalar quantity representing the total length of the path traveled.

What is magnitude in AP Physics C: Mechanics?

The size or amount of a quantity, often represented as the length of a vector arrow.

What is position in AP Physics C: Mechanics?

A vector quantity that specifies the location of an object relative to a reference point.

What is position vector in AP Physics C: Mechanics?

A vector denoted by r⃗ that specifies the location of a point relative to the origin.

What is resultant vector in AP Physics C: Mechanics?

The vector sum obtained by adding the components of two or more vectors.

What is scalar in AP Physics C: Mechanics?

A physical quantity that has only magnitude and no direction.

AP Physics C: Mechanics Vocabulary – 370 terms & definitions

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⚙️AP Physics C: Mechanics
Key Terms

250 essential vocabulary terms and definitions to know for your AP Physics C: Mechanics exam

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⚙️AP Physics C: Mechanics

Key Terms by Unit

📚Unit 1 – Kinematics

1.1 Scalars and Vectors

Term	Definition
acceleration	A vector quantity that describes the rate of change of an object's velocity with respect to time.
component	The projection of a vector along a specific direction, such as the x-, y-, or z-direction.
direction	The orientation or path along which a vector quantity acts.
displacement	A vector quantity representing the change in position from an initial to a final location.
distance	A scalar quantity representing the total length of the path traveled.
magnitude	The size or amount of a quantity, often represented as the length of a vector arrow.
position	A vector quantity that specifies the location of an object relative to a reference point.
position vector	A vector denoted by r⃗ that specifies the location of a point relative to the origin.
resultant vector	The vector sum obtained by adding the components of two or more vectors.
scalar	A physical quantity that has only magnitude and no direction.
speed	A scalar quantity representing the rate of change of distance with respect to time.
unit vector notation	A method of expressing vectors as the sum of their components in the x-, y-, and z-directions using unit vectors î, ĵ, and k̂.
vector	A quantity that has both magnitude and direction, used to represent forces on a free-body diagram.
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.

1.2 Displacement, Velocity, and Acceleration

Term	Definition
average acceleration	The change in velocity of an object divided by the time interval over which that change occurs.
average value	The mean value of a quantity calculated over a time interval.
average velocity	The displacement of an object divided by the time interval over which that displacement occurs.
derivative	A mathematical operation that represents the rate of change of a function with respect to a variable.
differentiation	The mathematical process of finding the derivative of a function.
displacement	A vector quantity representing the change in position from an initial to a final location.
instantaneous acceleration	The acceleration of an object at a specific instant in time, calculated as the limit of average acceleration over an infinitesimally small time interval.
instantaneous position	The exact location of an object at a specific moment in time.
instantaneous velocity	The velocity of an object at a specific instant in time, calculated as the limit of average velocity over an infinitesimally small time interval.
integration	The mathematical process of finding the antiderivative or accumulated sum of a function.
object model	A simplified representation of an object where size, shape, and internal configuration are ignored, treating the object as a single point with properties such as mass and charge.
position	A vector quantity that specifies the location of an object relative to a reference point.
time-dependent functions	Mathematical functions in which the output depends on time as the independent variable.

1.3 Representing Motion

Term	Definition
acceleration	A vector quantity that describes the rate of change of an object's velocity with respect to time.
constant acceleration	Motion in which an object's acceleration remains unchanged over time.
displacement	A vector quantity representing the change in position from an initial to a final location.
gravitational acceleration	The constant downward acceleration experienced by 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, calculated as the limit of average acceleration over an infinitesimally small time interval.
instantaneous velocity	The velocity of an object at a specific instant in time, calculated as the limit of average velocity over an infinitesimally small time interval.
kinematic equations	Mathematical equations that describe the motion of an object under constant acceleration in one dimension.
motion diagrams	Visual representations showing an object's position at successive time intervals to illustrate its motion.
position	A vector quantity that specifies the location of an object relative to a reference point.
velocity	A vector quantity that describes the rate of change of an object's position with respect to time.

1.4 Reference Frames and Relative Motion

Term	Definition
acceleration	A vector quantity that describes the rate of change of an object's velocity with respect to time.
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.
observer	A person or point of measurement from which physical quantities are measured and described in a particular reference frame.
reference frame	A coordinate system or perspective from which an observer measures the position, velocity, and other physical quantities of objects.
vector addition	The mathematical process of combining two or more vectors to find a resultant vector.
velocity	A vector quantity that describes the rate of change of an object's position with respect to time.

1.5 Motion in Two or Three Dimensions

Term	Definition
acceleration	A vector quantity that describes the rate of change of an object's velocity with respect to time.
component	The projection of a vector along a specific direction, such as the x-, y-, or z-direction.
kinematic relationships	Mathematical equations that describe the relationships between position, velocity, acceleration, and time for moving objects.
motion in three dimensions	The movement of an object that changes position in three perpendicular directions simultaneously.
motion in two dimensions	The movement of an object that changes position in two perpendicular directions simultaneously.
projectile motion	A special case of two-dimensional motion where an object experiences zero acceleration in one dimension and constant, nonzero acceleration in the perpendicular dimension.
velocity	A vector quantity that describes the rate of change of an object's position with respect to time.

📚Unit 2 – Force and Motion Dynamics

2.1 Properties and Interactions of a System

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.

2.10 Circular Motion

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.

2.2 Forces and Free-Body Diagrams

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.

2.3 Newton's Third Law

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.

2.4 Newton's First Law

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.

2.5 Newton's Second Law

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.

2.6 Gravitational Force

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.

2.7 Kinetic and Static Friction

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.

2.8 Spring Forces

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.

2.9 Resistive Forces

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.

📚Unit 3 – Work, Energy, and Power

3.1 Translational Kinetic Energy

Term	Definition
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.
reference frame	A coordinate system or perspective from which an observer measures the position, velocity, and other physical quantities of objects.
scalar	A physical quantity that has only magnitude and no direction.

3.2 Work

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 the entire mass can be considered to be concentrated for the purposes of analyzing motion and forces.
conservative force	A force for which the work done is path-independent and depends only on the initial and final configurations of the system.
displacement	A vector quantity representing the change in position from an initial to a final location.
dot product	A mathematical operation between two vectors that results in a scalar quantity equal to the product of their magnitudes and the cosine of the angle between them.
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 total energy of a system due to its motion and position, equal to the sum of 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 only magnitude and no direction.
work	Energy transferred to or from a system by forces or torques acting on it.
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.

3.3 Potential Energy

Term	Definition
conservative force	A force for which the work done is path-independent and depends only on the initial and final configurations of the system.
elastic potential energy	The potential energy stored in a spring due to its displacement from equilibrium, given by Us = 1/2 k(Δx)².
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.
ideal spring	A theoretical spring that obeys Hooke's law and stores elastic potential energy proportional to the square of its displacement.
local maximum	A point on a potential energy graph where the potential energy is higher than at nearby positions, corresponding to unstable equilibrium.
local minimum	A point on a potential energy graph where the potential energy is lower than at nearby positions, corresponding to stable equilibrium.
potential energy	The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces.
relaxed length	The natural length of a spring when no external force is applied to it.
scalar	A physical quantity that has only magnitude and no direction.
stable equilibrium	A position where a small displacement results in a restoring force that accelerates the object back toward the equilibrium position.
system	A defined collection of objects whose energy and interactions are being analyzed.
unstable equilibrium	A position where a small displacement results in a force that accelerates the object further away from the equilibrium position.
zero potential energy	A reference point chosen by an observer to simplify analysis of a system's potential energy.

3.4 Conservation of 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.
conservative force	A force for which the work done is path-independent and depends only on the initial and final configurations of the system.
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 process by which energy moves into or out of a system through the action of forces or torques.
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 total energy of a system due to its motion and position, equal to the sum of kinetic and potential energies.
nonconservative interactions	Interactions within a system, such as friction or air resistance, that dissipate mechanical energy as heat or other forms of energy.
potential energy	The energy stored in a system due to the relative positions or configurations of objects that interact via conservative forces.
system	A defined collection of objects whose energy and interactions are being analyzed.
work	Energy transferred to or from a system by forces or torques acting on it.

3.5 Power

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 process by which energy moves into or out of a system through the action of forces or torques.
instantaneous power	The rate at which energy is being transferred or converted at a specific instant in time.
power	The rate at which energy is transferred into or out of a system, or converted from one type to another within a system.
work	Energy transferred to or from a system by forces or torques acting on it.

📚Unit 4 – Linear Momentum

4.1 Linear Momentum

Term	Definition
collision	An interaction between objects where the forces exerted between them are much larger than any net external force on the system during the interaction.
explosion	An interaction in which internal forces within a system move objects apart from each other.
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.
object model	A simplified representation of an object where size, shape, and internal configuration are ignored, treating the object as a single point with properties such as mass and charge.
vector quantity	A physical quantity that has both magnitude and direction, such as momentum or velocity.

4.2 Change in Momentum and Impulse

Term	Definition
change in momentum	The difference between an object's final momentum and its initial momentum, represented as Δp = p - p₀.
impulse	A vector quantity representing the change in momentum of an object or system, calculated as the integral of net force over a time interval or the area under a force-time graph.
impulse-momentum theorem	The relationship stating that the impulse exerted on an object equals its change in momentum.
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.
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.
rate of change of momentum	The time derivative of momentum, which equals the net external force exerted on a system.
vector quantity	A physical quantity that has both magnitude and direction, such as momentum or velocity.

4.4 Elastic and Inelastic Collisions

Term	Definition
elastic collision	A collision between objects in which the total kinetic energy of the system is conserved, with initial kinetic energy equal to final kinetic energy.
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.
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 objects stick together after impact and move with the same velocity.

📚Unit 5 – Torque and Rotational Motion

5.1 Rotation

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.

5.2 Connecting Linear and Rotational Motion

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.

5.3 Torque

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.

5.4 Rotational Inertia

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.

5.5 Rotational Equilibrium and Newton's First Law in Rotational Form

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.

5.6 Newton's Second Law in Rotational Form

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.

📚Unit 6 – Rotating Systems: Energy & Momentum

6.1 Rotational Kinetic Energy

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.

6.2 Torque and Work

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.

6.3 Angular Momentum and Angular Impulse

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.

6.4 Conservation of Angular Momentum

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.

6.5 Kinetic Energy of a System with Translational and Rotational Motion

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.

6.6 Motion of Orbiting Satellites

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.

📚Unit 7 – Oscillations

7.1 Defining Simple Harmonic Motion (SHM)

Term	Definition
displacement	A vector quantity representing the change in position from an initial to a final location.
equilibrium position	The position where the spring force on an object is zero and the object-spring system is at rest.
periodic motion	Motion that repeats at regular intervals of time.
restoring force	A force exerted in a direction opposite to an object's displacement from its equilibrium position, acting to return the object to equilibrium.
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.

7.2 Frequency and Period of SHM

Term	Definition
angular frequency	The rate of change of phase angle in simple harmonic motion, denoted by ω and related to frequency by ω = 2πf.
frequency	The number of complete oscillations or cycles of simple harmonic motion that occur per unit time, 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 special case of a physical pendulum in which the hanging object is modeled as a point mass at a fixed distance from the pivot point.

7.3 Representing and Analyzing SHM

Term	Definition
acceleration	A vector quantity that describes the rate of change of an object's velocity with respect to time.
amplitude	The maximum displacement of an object from its equilibrium position in simple harmonic motion.
angular frequency	The rate of change of phase angle in simple harmonic motion, denoted by ω and related to frequency by ω = 2πf.
displacement	A vector quantity representing the change in position from an initial to a final location.
equilibrium position	The position where the spring force on an object is zero and the object-spring system is at rest.
extrema	The maximum and minimum values of displacement, velocity, or acceleration in simple harmonic motion.
frequency	The number of complete oscillations or cycles of simple harmonic motion that occur per unit time, measured in hertz (Hz).
natural frequency	The frequency at which a system will oscillate when displaced from its equilibrium position in the absence of external driving forces.
period	The time required for an object to complete one full circular path, rotation, or cycle.
phase constant	A constant (φ) in the equation x = A cos(ωt + φ) that determines the initial position and velocity of an object in simple harmonic motion.
resonance	The phenomenon where an oscillating system experiences maximum amplitude when driven by an external force at its natural frequency.
velocity	A vector quantity that describes the rate of change of an object's position with respect to time.

7.4 Energy of Simple Harmonic Oscillators

Term	Definition
amplitude	The maximum displacement of an object from its equilibrium position in simple harmonic motion.
conservation of energy	The principle that total mechanical energy remains constant in an isolated gravitational 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.
mechanical energy	The total energy of a system due to its motion and position, equal to the sum of 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 energy	The sum of kinetic and potential energies in a system exhibiting SHM, which remains constant over time.

7.5 Simple and Physical Pendulums

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.
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.
equilibrium position	The position where the spring force on an object is zero and the object-spring system is at rest.
moment of inertia	A measure of a rigid body's resistance to rotational acceleration about a given axis, represented by the symbol I.
physical pendulum	A rigid body that exhibits simple harmonic motion when displaced from its equilibrium position and allowed to oscillate.
restoring torque	The torque that acts to return a displaced physical pendulum back toward its equilibrium position.
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 special case of a physical pendulum in which the hanging object is modeled as a point mass at a fixed distance from the pivot point.
small-angle approximation	The approximation that sin(θ) ≈ θ for small angular displacements, used to simplify the analysis of pendulum motion.
torsion pendulum	A system undergoing simple harmonic motion where the restoring torque is proportional to the angular displacement of a rotating system.