University Physics Ch 01: Units, Physical Quantities & Vectors Practice Flashcards

Comprehensive vocabulary flashcards covering math review, S.I. units, significant figures, and vector mechanics for University Physics.

Base (Exponents)

The number and/or variable being multiplied in an exponential expression.

Exponent (Power)

The value representing how many times the base is multiplied.

Product Rule (Exponents)

The rule stating that when multiplying the same bases, the exponents are added ($a^m \times a^n = a^{m+n}$).

Quotient Rule (Exponents)

The rule stating that when dividing the same bases, the exponents are subtracted ($\frac{a^m}{a^n} = a^{m-n}$).

Zero Exponent Rule

The rule stating that anything raised to the zero exponent equals 1 ($a^0 = 1$).

Negative Exponent Rule

The rule stating that a negative exponent in the top moves to the bottom with a positive exponent, and a negative exponent in the bottom moves to the top ($a^{-n} = \frac{1}{a^n}$).

Power Rule (Exponents)

The rule stating that when raising a power to another power, the exponents are multiplied ($(a^m)^n = a^{m \cdot n}$).

Slope ($m$)

A number representing how steep a line is, calculated as $\frac{\text{rise}}{\text{run}}$ or $\frac{\Delta y}{\Delta x}$.

Quadratic Formula

The formula used to solve for $x$ in equations in the form $ax^2 + bx + c = 0$, expressed as $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Directly Proportional

A relationship between variables where as $x$ increases, $y$ increases ($y = 2x$).

Inversely Proportional

A relationship between variables where as $x$ increases, $y$ decreases ($y = \frac{1}{x}$).

Sine (S.O.H.)

A trigonometric function relating angles and sides of a right triangle where $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.平衡方

Cosine (C.A.H.)

A trigonometric function relating angles and sides of a right triangle where $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.平衡方

Tangent (T.O.A.)

A trigonometric function relating angles and sides of a right triangle where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.平衡方

Pythagorean Theorem

The geometric formula used for right triangles stating $a^2 + b^2 = c^2$.

Derivative

The instantaneous rate of change of a function, graphically representing the slope of a tangent line at a specific point.

Integral

Graphically represents the area under a curve and is mathematically the reverse of a derivative.

S.I. Units

The Système International grouping of compatible units used in Physics, such as Kilograms for Mass, Meters for Length, and Seconds for Time.

Metric Prefix

A letter or symbol representing a specific power of 10 used before a base unit, such as Kilo- ($10^3$) or Milli- ($10^{-3}$).

Scientific Notation

A method used to shorten very long numbers into the format $A.BC \times 10^D$, where the coefficient is at least 1 but less than 10.

Dimensional Analysis

The process of ensuring equations are dimensionally consistent by verifying that units on both sides of an equation match.

Density ($\rho$)

A physical quantity defined as mass divided by volume ($\rho = \frac{m}{V}$).

Scalar

A measurement that has magnitude only, such as temperature, time, or mass.

Vector

A measurement that has both magnitude and direction, such as force or displacement.

Distance ($d$)

A scalar quantity representing the magnitude of all lengths traveled.

Displacement ($\Delta \vec{x}$)

A vector quantity representing the change in position between the initial and final points.

Resultant Vector

The vector ($\vec{C}$ or $\vec{R}$) representing the shortest path from the start of the first vector to the end of the last vector.

Vector Decomposition

The process of breaking a 2D vector down into its 1D horizontal ($x$) and vertical ($y$) components using trigonometry.

Absolute Angle

The positive angle measurement of a vector starting from the positive $x$-axis.

Unit Vectors ($\hat{i}, \hat{j}, \hat{k}$)

Special vectors with a magnitude of 1 that point in the $x$, $y$, and $z$ directions respectively.

Dot Product (Scalar Product)

The multiplication of two vectors resulting in a scalar, calculated as the product of parallel components or $|A| |B| \cos(\theta)$.

Cross Product (Vector Product)

The multiplication of two vectors resulting in a new vector perpendicular to both, with magnitude calculated as $|A| |B| \sin(\theta)$.

Right-Hand Rule

A technique for determining the direction of a cross product vector by pointing fingers along the first vector and curling them toward the second.