Linear Kinematics Vocabulary

Vocabulary flashcards covering key concepts, coordinate systems, motion types, vectors, scalar quantities, and kinematical formulas from Chapter 2 Linear Kinematics.

Kinematics

The measurement of movement (derived from 'kine' meaning movement and 'matics' meaning measure), describing motion through position, velocity, and acceleration in linear and angular forms.

Position

An object's location in space, requiring a reference point or origin to be described.

Cartesian Coordinate System

A coordinate system that specifies an object's location in space using $X$ and $Y$ coordinates relative to a fixed reference point (origin).

Polar Coordinate System

A coordinate system that describes position using $r$ (resultant length) and $\theta$ (angle from origin), with spatial components defined by $X = r \times \tan(\theta)$ or $X = r \times \frac{\text{adjacent}}{\text{hypotenuse}}$ and $Y = r \times \frac{\text{opposite}}{\text{hypotenuse}}$ (specifically $X = r \times \text{cos}(\theta)$ and $Y = r \times \text{sin}(\theta)$).

Linear Motion

Also known as translation, motion in which all points on an object move the exact same distance; it includes rectilinear and curvilinear forms.

Rectilinear Motion

Linear motion in which there is no change in either the direction of motion or the orientation of the object during movement.

Curvilinear Motion

Linear motion involving a change in the direction of motion while maintaining no change in the orientation of the object.

Angular Motion

Also known as rotation, motion occurring about an axis within or outside the body, characterized by continual change of orientation where all points follow circular paths centered on the same axis.

General Motion

A combination of linear motion (translation) and angular motion (rotation).

Scalar

A physical quantity completely described by its magnitude alone, containing no direction and no negative value (e.g., mass, time, distance, speed).

Vector

A physical quantity described by both its magnitude and direction (e.g., displacement, velocity, acceleration).

Tail-to-Tip Method

A graphical vector addition approach where the tail of one vector is translated to the tip of another, creating a resultant vector connecting the initial tail to the final tip.

Decomposition Method

A mathematical approach to vector addition where each vector is resolved into $X$ and $Y$ components using polar coordinates, summed into $R_x$ and $R_y$, and combined at right angles using the Pythagorean theorem.

Distance Traveled

A scalar measure of the total length of the path followed by an object from its starting position to its ending position, designated by the symbol $l$.

Resultant Displacement

A vector quantity representing the length and direction measured in a straight line directly from an object's initial position to its final position, designated by the symbol $d$.

Speed

A scalar quantity representing the rate of motion or rate of change of distance traveled over time.

Average Speed

The ratio of total distance traveled to the total time interval, calculated using the formula \bar{s} = \frac{l}{\text{\textDelta} t}.

Velocity

A vector quantity representing the rate of change of resultant displacement over time, containing both magnitude and direction.

Average Velocity

Resultant displacement divided by the elapsed time interval, calculated using the formula \bar{v} = \frac{d}{\text{\textDelta} t} = \frac{d}{(t_f - t_i)}.

Acceleration

A vector quantity representing the rate of change of velocity over time, indicating the existence of force (\text{\textSigma} F = m \times a).

Average Acceleration

The change in velocity divided by the time interval over which it occurred, calculated as \bar{a} = \frac{\text{\textDelta} v}{\text{\textDelta} t} = \frac{v_f - v_i}{\text{\textDelta} t}.

Instantaneous Speed

The speed of an object measured at a single, specific instant in time.

Instantaneous Velocity

The velocity of an object at a specific instant in time, calculated as v = \text{lim} \frac{d}{\text{\textDelta} t} or represented by the slope of a tangent line on a position-time graph.

Tangential Method

A graphical method using the slope of tangent lines on a motion graph to determine instantaneous values (velocity from a displacement graph or acceleration from a velocity graph).