AP Physics C: Mechanics Vocabulary

Acceleration

The rate of change of velocity with respect to time, a = dv/dt; a vector quantity measured in m/s².

Example: "A car increasing its speed from 0 to 60 mph experiences a positive          in the direction of motion."

Amplitude

The maximum displacement of an oscillating object from its equilibrium position.

Example: "The          of the pendulum's swing decreased over time due to air resistance."

Angular Acceleration

The rate of change of angular velocity with respect to time, α = dω/dt, measured in rad/s².

Similar definitions: rotational acceleration

Example: "When the spinning wheel slowed down, it experienced a negative         ."

Angular Displacement

The angle through which an object rotates about a fixed axis, measured in radians.

Example: "After two full rotations, the wheel had an          of 4π radians."

Angular Frequency

The rate of change of the oscillation phase, related to frequency by ω = 2πf, measured in rad/s.

Example: "The          of the mass-spring system determines how rapidly it oscillates."

Angular Impulse

The product of torque and the time interval over which it acts, equal to the change in angular momentum: ΔL = τΔt.

Example: "The          delivered by the brake pad brought the rotating disc to a stop."

Angular Momentum

The rotational analog of linear momentum, defined as L = Iω for rigid bodies or L = r × p for a particle; conserved when net external torque is zero.

Example: "An ice skater pulling in her arms reduces her moment of inertia and increases her angular velocity, conserving         ."

Angular Velocity

The rate of change of angular displacement with respect to time, ω = dθ/dt, measured in rad/s.

Similar definitions: rotational velocity

Example: "The          of the merry-go-round increased as more force was applied."

Atwood Machine

A device consisting of two masses connected by a string over a pulley, used to study Newton's second law and acceleration due to unbalanced forces.

Example: "In the         , the heavier mass accelerates downward while the lighter mass accelerates upward."

Average Acceleration

The change in velocity divided by the elapsed time interval: a_avg = Δv/Δt.

Example: "The          of the sprinter was calculated by dividing the change in speed by the time taken."

Average Velocity

The total displacement divided by the total time elapsed: v_avg = Δx/Δt.

Example: "Although the car sped up and slowed down, its          over the entire trip was 50 km/h."

Banked Curve

A curved road or track tilted at an angle to the horizontal so that the normal force provides a component of centripetal force, reducing reliance on friction.

Example: "On a frictionless         , the car can navigate the turn at a specific speed determined by the bank angle and radius."

Center of Gravity

The point at which the total gravitational torque on a body is zero; coincides with the center of mass when the gravitational field is uniform.

Example: "For an object in a uniform gravitational field, the          is at the same location as the center of mass."

Center of Mass

The mass-weighted average position of a system, found by integration for continuous bodies; it moves as though all external forces act on it.

Example: "The          of the two-object system followed a parabolic trajectory even as the objects spun apart."

Centripetal Acceleration

The acceleration directed toward the center of a circular path, with magnitude a_c = v²/r = ω²r.

Example: "As the car rounded the curve, the          kept it on the circular path."

Centripetal Force

The net inward force that causes an object to follow a curved or circular path, directed toward the center of curvature; not a separate force but the resultant of real forces.

Example: "Tension in the string provides the          needed to keep the ball moving in a circle."

Closed System

A system on which no external forces act, allowing conservation of momentum and energy to apply.

Similar definitions: isolated system

Example: "In a         , the total momentum before and after a collision remains the same."

Coefficient of Friction

A dimensionless scalar that characterizes the ratio of the friction force between two surfaces to the normal force pressing them together.

Example: "Ice has a very low         , which is why objects slide easily on its surface."

Conical Pendulum

A pendulum in which the bob moves in a horizontal circle while the string traces out a cone; the tension provides both the vertical support and the centripetal force.

Example: "In a         , the bob's speed and the string angle determine the radius of the circular path."

Conservation of Angular Momentum

The total angular momentum of a system remains constant when no net external torque acts on it: dL/dt = 0 when τ_net = 0.

Example: "The          explains why a spinning figure skater speeds up when pulling her arms inward."

Conservation of Energy

The total energy of an isolated system remains constant; energy can be transformed from one form to another but cannot be created or destroyed.

Example: "Using the principle of         , we can equate the potential energy at the top of a hill to the kinetic energy at the bottom."

Conservation of Linear Momentum

The total momentum of a closed system remains constant in the absence of external forces: dp/dt = 0 when F_net = 0.

Example: "The          allows us to predict the velocities of objects after a collision."

Conservative Force

A force for which the work done is path-independent and depends only on the initial and final positions; a potential energy function can be defined for it.

Example: "Gravity is a          because the work it does on an object depends only on the change in height, not the path taken."

Cross Product

A vector operation on two vectors that yields a third vector perpendicular to both, with magnitude |A × B| = AB sin θ; used for torque and angular momentum.

Similar definitions: vector product

Example: "Torque is calculated using the          of the position vector and the force vector."

Damped Oscillation

Oscillatory motion in which a non-conservative force (such as friction or drag) causes the amplitude to decrease over time.

Example: "The pendulum exhibited          as air resistance gradually reduced the height of each swing."

Derivative

A calculus operation that gives the instantaneous rate of change of a function; in mechanics, velocity is the derivative of position and acceleration is the derivative of velocity.

Example: "Taking the          of the position function x(t) with respect to time gives the velocity function v(t)."

Differential Equation

An equation involving derivatives of an unknown function; many physical laws in AP Physics C are expressed this way, such as F = m(dv/dt) and the SHM equation d²x/dt² = −(k/m)x.

Example: "The equation of motion for a mass on a spring is a second-order          whose solution is a sinusoidal function."

Displacement

A vector quantity representing the change in position of an object; the straight-line distance and direction from the initial to the final position.

Example: "Even though the runner completed a full lap, her          was zero because she returned to her starting point."

Dot Product

A scalar operation on two vectors that yields a number equal to A · B = AB cos θ; used to calculate work and power.

Similar definitions: scalar product

Example: "Work is calculated using the          of the force and displacement vectors."

Drag Force

A resistive force that opposes the motion of an object through a fluid, depending on the object's speed, shape, and the fluid's properties.

Similar definitions: air resistance, fluid resistance

Example: "At terminal velocity, the          equals the gravitational force on the falling object."

Dynamic Equilibrium

A state in which an object moves with constant velocity (both translational and rotational) because the net force and net torque are both zero.

Example: "A car cruising at constant speed on a straight highway is in          because the driving force balances friction and drag."

Elastic Collision

A collision in which both momentum and kinetic energy are conserved; the objects bounce off each other without permanent deformation.

Example: "In an ideal          between two billiard balls, no kinetic energy is lost to heat or sound."

Elastic Potential Energy

Energy stored in a deformed elastic object such as a spring, given by U = ½kx².

Similar definitions: spring potential energy

Example: "Compressing the spring stores          that is released when the spring returns to its natural length."

Energy Diagram

A graph of potential energy versus position used to analyze the motion of a particle; turning points occur where total energy equals potential energy, and equilibria occur at extrema of U(x).

Similar definitions: potential energy curve

Example: "By examining the         , we can identify stable and unstable equilibrium positions and the regions where the particle is confined."

Equilibrium

A state in which the net force and net torque on an object are both zero, so the object has no translational or rotational acceleration.

Similar definitions: mechanical equilibrium

Example: "A book resting on a table is in          because the normal force balances gravity."

Escape Velocity

The minimum speed an object must have to escape the gravitational pull of a planet without further propulsion, derived from energy conservation: v_e = √(2GM/r).

Example: "A rocket must reach          to leave Earth's gravitational field without additional thrust."

External Force

A force applied to a system from outside its boundary that can change the system's total momentum or mechanical energy.

Example: "Friction from the road is an          that slows the sliding crate and reduces its kinetic energy."

Fictitious Force

An apparent force that arises in a non-inertial (accelerating) reference frame; not caused by any physical interaction but needed to apply Newton's laws in that frame.

Similar definitions: pseudo force, inertial force

Example: "The centrifugal force felt by a passenger in a turning car is a          that appears only in the rotating reference frame."

Force

Any interaction that, when unopposed, changes the motion of an object; a vector quantity measured in newtons (N), related to momentum by F = dp/dt.

Example: "A net          acting on the block caused it to accelerate across the surface."

Forced Oscillation

Oscillation that occurs when an external periodic force is applied to a system, driving it at a particular frequency.

Example: "The child pushing the swing at regular intervals is an example of         ."

Free Body Diagram

A diagram showing all the forces acting on a single object, represented as arrows originating from the object's center of mass.

Similar definitions: force diagram

Example: "Drawing a          helps identify all forces on the block before applying Newton's second law."

Free Fall

Motion of an object under the influence of gravity alone, with no air resistance, accelerating at g ≈ 9.8 m/s² near Earth's surface.

Example: "An object in          near Earth accelerates downward at approximately 9.8 m/s²."

Frequency

The number of complete oscillations or cycles per unit time, measured in hertz (Hz), related to period by f = 1/T.

Example: "The          of the mass-spring system is f = (1/2π)√(k/m)."

Friction

A contact force that opposes the relative motion or tendency of motion between two surfaces; includes static and kinetic types.

Example: "         between the tires and the road allows the car to accelerate without slipping."

Gravitational Field

A region of space surrounding a mass in which another mass experiences a gravitational force; field strength g = GM/r² points toward the source mass.

Example: "The          around Earth weakens with increasing distance from its surface."

Gravitational Force

The attractive force between any two objects with mass, given by Newton's law of universal gravitation: F = Gm₁m₂/r².

Example: "The          between Earth and the Moon keeps the Moon in its orbit."

Gravitational Potential Energy

Energy stored due to an object's position in a gravitational field; near Earth's surface, U = mgh; in general, U = −GMm/r.

Example: "Lifting the ball to a greater height increases its         ."

Hooke's Law

The restoring force exerted by an ideal spring is proportional to its displacement from equilibrium and opposite in direction: F = −kx.

Example: "According to         , doubling the stretch of a spring doubles the restoring force."

Impulse

The integral of force over time, equal to the change in momentum: J = ∫F dt = Δp.

Example: "Catching a ball with soft hands increases the time of impact, reducing the force while delivering the same         ."

Impulse-Momentum Theorem

The net impulse on an object equals its change in momentum: J = Δp = ∫F_net dt.

Example: "The          explains why airbags reduce injury by increasing the time over which the stopping force is applied."

Inclined Plane

A flat surface tilted at an angle to the horizontal, used to analyze the components of gravitational force parallel and perpendicular to the surface.

Example: "On an         , the component of gravity along the slope causes the block to accelerate downward."

Inelastic Collision

A collision in which momentum is conserved but kinetic energy is not; some energy is converted to heat, sound, or deformation.

Example: "When two cars crash and crumple together, they undergo an          where kinetic energy is lost."

Inertia

The tendency of an object to resist changes in its state of motion; directly proportional to mass.

Example: "A heavy truck has more          than a bicycle, making it harder to start or stop."

Inertial Reference Frame

A frame of reference in which Newton's first law holds; that is, a frame that is not accelerating.

Example: "A lab at rest on Earth's surface is approximately an          for most mechanics problems."

Instantaneous Acceleration

The acceleration of an object at a specific instant in time, equal to the derivative of velocity with respect to time: a = dv/dt = d²x/dt².

Example: "The          can be found from the slope of the velocity-time graph at any point."

Instantaneous Power

The rate at which work is done at a specific instant: P = dW/dt = F · v.

Example: "The          delivered by the engine increased as the car's speed rose on the highway."

Instantaneous Velocity

The velocity of an object at a specific instant in time, equal to the derivative of position with respect to time: v = dx/dt.

Example: "The          of the ball at the peak of its trajectory is zero in the vertical direction."

Integral

A calculus operation that computes the accumulated total of a quantity; in mechanics, the integral of velocity gives displacement and the integral of force over displacement gives work.

Example: "The          of acceleration with respect to time from t₁ to t₂ yields the change in velocity over that interval."

Internal Force

A force between components within a system that does not change the system's total momentum but can redistribute energy among its parts.

Example: "The spring force between two carts in a system is an          that redistributes energy but conserves the system's total momentum."

Kepler's First Law

Each planet moves in an elliptical orbit with the Sun at one focus.

Similar definitions: law of ellipses

Example: "         explains why a planet's distance from the Sun varies throughout its orbit."

Kepler's Second Law

A line segment joining a planet to the Sun sweeps out equal areas in equal time intervals, a consequence of conservation of angular momentum.

Similar definitions: law of equal areas

Example: "         implies that a planet moves faster when it is closer to the Sun."

Kepler's Third Law

The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit: T² = (4π²/GM)a³.

Similar definitions: law of harmonies

Example: "Using         , astronomers can determine the orbital period of a planet from its distance to the Sun."

Kinematics

The branch of mechanics that describes the motion of objects using position, velocity, and acceleration without considering the forces that cause the motion.

Example: "         equations allow us to calculate position, velocity, and acceleration as functions of time."

Kinetic Energy

The energy an object possesses due to its motion, given by KE = ½mv² for translational motion.

Example: "A moving car has          that increases with the square of its speed."

Kinetic Friction

The friction force acting on an object that is already sliding across a surface; f_k = μ_k · N, where N is the normal force.

Similar definitions: sliding friction

Example: "         acts on the box as it slides across the floor, slowing it down."

Lever Arm

The perpendicular distance from the axis of rotation to the line of action of a force; determines the magnitude of the torque produced.

Similar definitions: moment arm

Example: "Pushing on a door near the hinge gives a short          and produces less torque than pushing near the handle."

Linear Momentum

The product of an object's mass and velocity: p = mv; a vector quantity measured in kg·m/s.

Similar definitions: momentum

Example: "A truck moving at low speed can have the same          as a small car moving at high speed."

Mass

A scalar quantity that measures the amount of matter in an object and its resistance to acceleration; the proportionality constant in F = ma.

Example: "An astronaut's          remains the same on the Moon, even though her weight is less."

Mechanical Energy

The sum of kinetic energy and potential energy in a system: E = KE + PE; conserved when only conservative forces do work.

Example: "In the absence of friction, the          of a pendulum remains constant throughout its swing."

Moment of Inertia

A measure of an object's resistance to rotational acceleration, depending on the distribution of mass relative to the axis of rotation: I = ∫r² dm for continuous bodies.

Similar definitions: rotational inertia

Example: "A hollow cylinder has a greater          than a solid cylinder of the same mass and radius because its mass is farther from the axis."

Net Force

The vector sum of all forces acting on an object; determines the object's acceleration via Newton's second law: ΣF = ma.

Similar definitions: resultant force

Example: "When the          on an object is zero, it remains at rest or moves with constant velocity."

Net Torque

The vector sum of all torques acting on an object; determines its angular acceleration: Στ = Iα.

Example: "When the          on a seesaw is zero, it remains balanced and does not rotate."

Newton's First Law

An object at rest stays at rest, and an object in motion continues with constant velocity, unless acted upon by a net external force.

Similar definitions: law of inertia

Example: "         explains why passengers lurch forward when a car suddenly brakes."

Newton's Law of Universal Gravitation

Every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = Gm₁m₂/r².

Example: "         allows us to calculate the gravitational attraction between any two masses in the universe."

Newton's Second Law

The net force on an object equals the rate of change of its momentum: F_net = dp/dt, which simplifies to F_net = ma when mass is constant.

Example: "According to         , doubling the force on an object doubles its acceleration if the mass stays constant."

Newton's Second Law for Rotation

The net torque on a rigid body equals its moment of inertia times its angular acceleration: Στ = Iα; the rotational analog of F = ma.

Example: "Applying          to a spinning disk allows us to find the angular acceleration produced by the applied torque."

Newton's Third Law

For every action force, there is an equal and opposite reaction force; the two forces act on different objects.

Similar definitions: action-reaction law

Example: "         explains why a rocket propels forward as exhaust gases are expelled backward."

Non-Conservative Force

A force for which the work done depends on the path taken; it converts mechanical energy into other forms such as heat.

Example: "Friction is a          because the work it does depends on the length of the path, not just the endpoints."

Non-Inertial Reference Frame

A reference frame that is accelerating, in which fictitious forces (such as centrifugal and Coriolis forces) appear to act on objects.

Example: "Inside a rotating carousel, objects seem to experience an outward push because it is a         ."

Non-Uniform Circular Motion

Circular motion in which the speed changes over time, so the object has both centripetal (radial) and tangential components of acceleration.

Example: "A ball swinging on a string in a vertical circle undergoes          because gravity changes its speed at different points in the loop."

Normal Force

The perpendicular contact force exerted by a surface on an object resting on it, preventing the object from passing through the surface.

Example: "The          on a book lying on a table is equal in magnitude to the book's weight when the table is horizontal."

Orbital Period

The time it takes for an object to complete one full orbit around another body, related to orbital radius by Kepler's third law.

Example: "The          of the International Space Station is approximately 90 minutes."

Orbital Velocity

The velocity needed for an object to maintain a stable circular orbit around a massive body: v = √(GM/r).

Example: "A satellite must travel at the correct          to remain in a stable orbit without falling to Earth or drifting away."

Parallel Axis Theorem

A formula for calculating the moment of inertia about any axis parallel to one through the center of mass: I = I_cm + Md².

Example: "The          was used to find the moment of inertia of the rod about a pivot at its end."

Pendulum

A mass suspended from a pivot that swings freely under gravity; for small angles, it undergoes simple harmonic motion with period T = 2π√(L/g).

Similar definitions: simple pendulum

Example: "The period of a simple          depends only on its length and the local gravitational acceleration, not on its mass."

Perfectly Inelastic Collision

A collision in which the objects stick together after impact and move with a common velocity; maximum kinetic energy is lost while momentum is conserved.

Example: "A football tackle where the players move together afterward is a         ."

Period

The time required for one complete cycle of oscillation or revolution, measured in seconds; T = 1/f.

Example: "The          of a mass on a spring is T = 2π√(m/k)."

Phase Constant

The constant φ₀ in the equation x(t) = A cos(ωt + φ₀) that determines the initial position and velocity of an oscillator at t = 0.

Similar definitions: initial phase, phase angle

Example: "The          is determined by the initial conditions of the oscillating system."

Physical Pendulum

An extended rigid body that oscillates about a pivot point; its period depends on the moment of inertia and the distance from the pivot to the center of mass: T = 2π√(I/mgd).

Example: "A swinging rod pivoted at one end is a          whose period differs from that of a simple pendulum of the same length."

Position Function

A mathematical expression x(t) that gives an object's position as a function of time; its first derivative gives velocity and its second derivative gives acceleration.

Example: "Given the          x(t) = 3t² − 2t + 1, we can find the velocity by differentiating with respect to time."

Potential Energy

Energy stored in a system due to the position or configuration of its components; defined so that F = −dU/dx for a conservative force in one dimension.

Example: "A stretched rubber band stores          that is released when it snaps back to its natural length."

Potential Energy Function

A function U(x) whose negative derivative gives the conservative force acting on a particle: F = −dU/dx; used in energy diagrams to analyze motion.

Example: "The          for a spring is U(x) = ½kx², from which the restoring force F = −kx is derived."

Power

The rate at which work is done or energy is transferred: P = dW/dt = F · v, measured in watts (W).

Example: "A more powerful engine can do the same amount of work in less time, meaning it has greater         ."

Projectile Motion

The motion of an object launched into the air, subject only to gravity, following a parabolic trajectory with constant horizontal velocity and constant vertical acceleration.

Example: "A ball kicked off a cliff undergoes          with constant horizontal velocity and increasing vertical velocity."

Pulley

A simple machine consisting of a wheel on an axle used to redirect a tension force; an ideal massless pulley changes direction without changing the tension magnitude.

Example: "An ideal massless          changes the direction of the tension force without changing its magnitude."

Range

The horizontal distance traveled by a projectile; for level ground, R = v₀² sin(2θ)/g.

Example: "The maximum          of a projectile launched from level ground is achieved at a 45° launch angle."

Reference Frame

A coordinate system used to describe the position and motion of objects; measurements of velocity and acceleration depend on the chosen frame.

Example: "The velocity of the ball is different when measured from a moving train's          versus the ground frame."

Relative Motion

The motion of an object as observed from a particular reference frame; different observers can measure different velocities for the same object.

Example: "The concept of          explains why a passenger in a moving train sees a tree moving backward."

Resonance

A condition in which the driving frequency of an external force matches the natural frequency of a system, producing maximum amplitude oscillation.

Example: "Soldiers break step when crossing a bridge to avoid          that could cause dangerous oscillations."

Restoring Force

A force that acts to bring a displaced object back toward its equilibrium position; in SHM, it is proportional to displacement: F = −kx.

Example: "In a mass-spring system, the          pulls the mass back toward the equilibrium point."