Physics Unit 1: Vectors, Measurement, and Mechanics

Vocabulary practice flashcards covering vector resolution, graphical and algebraic vector addition, dimensional analysis, units, centripetal force, and precision versus accuracy based on lecture notes and exam problems.

Accuracy

How close a measured value is to the true, actual, or accepted value; it focuses on correctness, can be evaluated with a single data point, is primarily impacted by systematic error (bias), and is statistically evaluated via percent error.

Precision

How close repeated measurements in a series are to each other, regardless of the true value; it focuses on consistency and repeatability, requires multiple measurements to assess, is primarily impacted by random error (noise), and is calculated via standard deviation or range.

Systematic Error (Bias)

A predictable or constant deviation that primarily affects accuracy by shifting measurements away from the true target value; it is corrected through recalibration of measuring instruments.

Random Error (Noise)

Unpredictable statistical fluctuations that primarily affect precision by causing scatter among repeated measurements; it is mitigated by expanding sample size.

Percent Error

The statistical metric used to calculate and assess the accuracy of an experimental measurement against an accepted or true reference value.

Standard Deviation and Range

The statistical metrics used to quantify the precision, consistency, and degree of scatter among a dataset of repeated measurements.

High Precision, Low Accuracy

A measurement state where data points are tightly clustered and repeatable but systematically off from the true value, exemplified by a certified $100\,\text{g}$ weight measuring $103.1\,\text{g}$, $103.2\,\text{g}$, and $103.1\,\text{g}$.

High Accuracy, Low Precision

A measurement state where the mathematical average of widely scattered readings matches the true value despite poor repeatability, exemplified by readings of $98.1\,\text{g}$, $101.9\,\text{g}$, and $100.0\,\text{g}$ for a certified $100\,\text{g}$ weight.

Dimensionless Physical Quantities

Physical ratios that carry no base SI units, specifically including refractive index, strain, and relative density.

Dimensional Analysis of $\frac{PQ}{R}$

The algebraic simplification of base units $P = \text{kg}\,\text{m}^{-3}$, $Q = \text{kg}\,\text{m}\,\text{s}^{-2}$, and $R = \text{kg}^2\,\text{m}^{-3}\,\text{s}^{-1}$, which simplifies to $\text{m}\,\text{s}^{-1}$ and represents the physical quantity speed.

Mass Conversion Relation ($x = 3\,\text{mg}$, $y = 9\,\text{kg}$)

The relationship expressing mass $y$ in terms of $x$ when $x = 3 \times 10^{-6}\,\text{kg}$ and $y = 9\,\text{kg}$, given by the equation $y = 3 \times 10^6 x$.

Resultant of Perpendicular Vectors ($12\,\text{N}$ North and $5\,\text{N}$ West)

A resultant vector having a magnitude of $13\,\text{N}$ directed northwest, calculated from the perpendicular vectors using the Pythagorean theorem: $\sqrt{(12\,\text{N})^2 + (5\,\text{N})^2} = \sqrt{144 + 25} = 13\,\text{N}$.

Graphical Method of Vector Addition

A method to find the resultant vector by drawing each vector tail-to-tip or using a parallelogram, where every vector must be drawn strictly to scale using a ruler and a protractor.

Vector Resolution into Components

The process of breaking down a vector $\mathbf{V}$ into perpendicular axes using trigonometry, where $V_x = V \cos(\theta)$ and $V_y = V \sin(\theta)$ when $\theta$ is measured relative to the positive $x$-axis.

Resultant Vector Magnitude Formula

The equation used to calculate the total magnitude of a resultant vector from its perpendicular component sums: $V = \sqrt{V_x^2 + V_y^2}$.

Resultant Vector Direction Angle Formula

The trigonometric formula used to find the orientation angle $\theta$ of a resultant vector relative to the horizontal axis: $\tan(\theta) = \frac{V_y}{V_x}$.

Airplane Three-Leg Displacement Problem

A vector problem combining legs of $620\,\text{km}$ due east, $440\,\text{km}$ southeast ($45^\circ$), and $550\,\text{km}$ at $53^\circ$ south of west, producing net components $V_x = 600\,\text{km}$ and $V_y = -750\,\text{km}$, and a total displacement of approximately $960\,\text{km}, 51^\circ\text{ south of east}$.

Car Two-Leg Displacement Problem

A vector problem combining a drive of $215\,\text{km}$ west and $85\,\text{km}$ southwest ($45^\circ$), yielding net components $V_x = -275\,\text{km}$ and $V_y = -60\,\text{km}$, resulting in a net displacement of $281\,\text{km}, 12^\circ\text{ S of W}$.

Centripetal Force Formula

The relationship $F = \frac{m (v)^2}{r}$ used to compute the inward force required to keep an object of mass $m$ moving at speed $v$ in a circular path of radius $r$.

Arbitrary Units Vector Addition ($\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$)

The component-method addition of three vectors—$\mathbf{A} = 440$ at $28^\circ$, $\mathbf{B} = 26.5$ at $56^\circ$ north of west, and $\mathbf{C} = 31.0$ south—yielding net components $\sum V_x = 373.7$ and $\sum V_y = 197.6$, giving a resultant magnitude of $428.04$ (or $423$) at $28^\circ$ above the positive $x$-axis.