PHY 101: General Physics - Units, Vectors, and One-Dimensional Kinematics

Vocabulary practice flashcards covering fundamental physical units, standards of measurement, dimensional analysis, vectors and vector operations, and one-dimensional kinematics based on PHY 101 lecture notes.

SI (Système International)

A set of metric standards established in 1960 by an international committee for the fundamental quantities of science, in which the fundamental units of length, mass, and time are the meter, kilogram, and second.

Length

The distance between two points in space. Its SI unit is the meter ($\text{m}$), defined such that the speed of light in vacuum is exactly $c = 2.9979458 \times 10^8\,\text{m/s} \approx 3.0 \times 10^8\,\text{m/s}$.

Kilogram ($\text{kg}$)

The SI fundamental unit of mass, defined on the basis of a specific standard cylinder kept at the International Bureau of Standards.

Second ($\text{s}$)

The SI fundamental unit of time, defined in terms of the oscillation of radiation from a cesium atom.

Dimension

A term in physics that denotes the physical nature of a quantity, typically denoted with square brackets such as length $[L]$, mass $[M]$, and time $[T]$.

Principle of Homogeneity

The principle stating that equations depicting physical situations must have identical dimensions on both sides throughout the equation (e.g., $[M]^a [L]^b [T]^c = [M]^x [L]^y [T]^z$).

Significant Figures

The number of reliably known numerical digits used to express a physical measurement, reflecting the experimental uncertainty of the apparatus and measurement procedure.

Plane Polar Coordinates ($r, \theta$)

A coordinate system representing a point in a plane by a radial distance $r$ from the origin and an angle $\theta$ measured counterclockwise from a fixed reference axis (usually the positive $x$-axis).

Scalar Quantity

A physical quantity that is completely specified by magnitude alone and has no direction (examples include temperature, volume, mass, and speed).

Vector Quantity

A physical quantity characterized by having both a magnitude and a direction in space (examples include displacement, velocity, and acceleration).

Equality of Two Vectors

The condition where two vectors have the exact same magnitude and point in the same direction along parallel lines, regardless of their starting positions in space.

Commutative Law of Vector Addition

The property stating that the order in which two vectors are added does not alter their resultant vector: $\vec{A} + \vec{B} = \vec{B} + \vec{A}$.

Associative Law of Vector Addition

The property stating that the grouping of vectors does not affect the final sum: $\vec{A} + (\vec{B} + \vec{C}) = (\vec{A} + \vec{B}) + \vec{C}$.

Dot (Scalar) Product

The algebraic operation between two vectors $\vec{A}$ and $\vec{B}$ resulting in a scalar defined by $\vec{A} \cdot \vec{B} = AB\cos(\theta)$, where $\theta$ is the angle between them ($0 \le \theta \le \pi$).

Cross (Vector) Product

The algebraic operation between two vectors $\vec{A}$ and $\vec{B}$ yielding a vector $\vec{C} = \vec{A} \times \vec{B}$ with magnitude $AB\sin(\theta)$ and direction perpendicular according to a unit vector $\mathbf{u}$, satisfying the anti-commutative property $\vec{A} \times \vec{B} = -(\vec{B} \times \vec{A})$.

Kinematics

The branch of classical mechanics that describes the motion of objects while ignoring the interactions with external agents that might cause or modify that motion.

Particle

A point-like object used in physics modeling that possesses mass but has infinitesimal spatial size.

Position ($x$)

The location of a particle in space with respect to a chosen reference point defined as the origin of a coordinate system.

Displacement ($\Delta x$)

The change in position of a particle during a time interval, given by $\Delta x = x_f - x_i$, which can take either positive or negative values.

Distance

A scalar physical quantity representing the total length of the path followed by a moving particle, always expressed as a positive number.

Average Velocity ($v_{x,\text{avg}}$;)

A vector quantity defined as the displacement $\Delta x$ divided by the time interval $\Delta t$ during which that displacement occurs: $v_{x,\text{avg}} = \frac{\Delta x}{\Delta t}$.

Average Speed ($v_{\text{avg}}$;)

A scalar quantity defined as the total distance $d$ traveled divided by the total time interval $\Delta t$ required to travel that distance: $v_{\text{avg}} = \frac{d}{\Delta t}$.

Instantaneous Velocity ($v_x$)

The velocity of a particle at a specific instant in time, defined mathematically as the limiting value of the average velocity as $\Delta t$ approaches zero: $v_x = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$.

Instantaneous Speed

A scalar quantity defined as the absolute magnitude of the instantaneous velocity of a particle at a given moment.

Average Acceleration ($a_{x,\text{avg}}$;)

The ratio of the change in velocity $\Delta v_x$ to the time interval $\Delta t$ during which that change takes place: $a_{x,\text{avg}} = \frac{\Delta v_x}{\Delta t} = \frac{v_{xf} - v_{xi}}{t_f - t_i}$.

Instantaneous Acceleration ($a_x$)

The limit of average acceleration as the time interval $\Delta t$ approaches zero, equal to the instantaneous rate of change of velocity with respect to time: $a_x = \lim_{\Delta t \to 0} \frac{\Delta v_x}{\Delta t} = \frac{dv_x}{dt}$.

Constant Acceleration

A state of motion wherein the acceleration of a particle remains constant in both magnitude and direction ($a = \text{constant}$), meaning velocity changes by equal amounts in equal intervals of time.