S1 Physics Study Guide: Chapters 1 & 2 Newtonian Paradigm and Uncertainties

100 comprehensive vocabulary flashcards covering causal reasoning, Newtonian mechanics, units, vectors, gravitation, equilibrium, pressure, forces, experimental variables, uncertainties, statistical spread, and mathematical modeling.

Scientific Method

The systematic approach in physics using observations, measurements, models, hypotheses, experiments, and repeated testing to identify causes and effects.

Causal Explanation

A scientific explanation that connects a change in one quantity to a resulting change in another while controlling other relevant factors.

Newtonian Mechanics

The branch of physics that describes motion by relating external forces to acceleration.

Average Speed

The rate at which distance changes over time, calculated using the formula $\text{speed} = \frac{\text{distance}}{\text{time}}$, with SI unit $\text{m}\,\text{s}^{-1}$.

Speed Unit Conversion

The conversion equivalence between metres per second and kilometres per hour, where $1\,\text{m}\,\text{s}^{-1} = 3.6\,\text{km}\,\text{h}^{-1}$.

Acceleration

A physical quantity describing how quickly velocity changes over time, measured in the SI unit $\text{m}\,\text{s}^{-2}$.

Introductory One-Dimensional Acceleration

The acceleration in one dimension defined as $a = \frac{\text{change in speed}}{\text{time}}$, with unit $\text{m}\,\text{s}^{-2}$.

First SUVAT Relation

The kinematic relationship $v = at + u$, where $u$ is initial velocity, $v$ is final velocity, $a$ is constant acceleration, and $t$ is time.

SI Prefix Kilo

An SI prefix indicating a power of ten equal to $10^3$.

SI Prefix Centi

An SI prefix indicating a power of ten equal to $10^{-2}$.

SI Prefix Milli

An SI prefix indicating a power of ten equal to $10^{-3}$.

SI Prefix Micro

An SI prefix indicating a power of ten equal to $10^{-6}$.

SI Prefix Nano

An SI prefix indicating a power of ten equal to $10^{-9}$.

Significant Figures

Digits that communicate the precision of measurements, indicating that calculated results should not be reported with more precision than input data supports.

Order-of-Magnitude Estimates

Back-of-the-envelope calculations using rounded values to quickly check whether a calculated result is reasonable.

Newton's Second Law of Motion

The physical law stating that acceleration is caused by the resultant external force and depends on mass: $a = \frac{F_{\text{net}}}{m}$, or equivalently $F_{\text{net}} = ma$.

Mass

A fundamental quantity that measures the amount of matter in an object and its resistance to acceleration.

Inertia

An object's inherent resistance to acceleration or changes in its state of motion.

Density ($\rho$)

Mass per unit volume, defined by the formula $\rho = \frac{m}{V}$.

Rearranged Density Relation

The equation expressing mass in terms of density and volume: $m = \rho V$.

SI Base Units

The foundational units of the SI system, including the kilogram ($\text{kg}$), metre ($\text{m}$), second ($\text{s}$), and ampere ($\text{A}$).

Derived Units

Measurement units formed by algebraic combinations of SI base units.

Newton ($\text{N}$)

The derived SI unit of force, defined in terms of base units as $1\,\text{N} = 1\,\text{kg}\,\text{m}\,\text{s}^{-2}$.

Scalar

A physical quantity that has magnitude only, such as mass, time, distance, speed, and energy.

Vector

A physical quantity that possesses both magnitude and direction, such as displacement, velocity, acceleration, and force.

Resultant Vector

The vector sum of two or more vectors, which must be computed by accounting for both their magnitudes and directions.

Net Force ($F_{\text{net}}$)

The vector sum of all external forces acting on an object: $F_{\text{net}} = \sum F$.

Balanced Forces

A condition where multiple forces acting on the same object sum to a zero resultant, producing no acceleration.

Two-Dimensional Force Resolution

Resolving vectors into perpendicular components to apply Newton's 2nd law independently in each direction: $m a_x = (F_{\text{net}})_x$ and $m a_y = (F_{\text{net}})_y$.

Universal Gravitation

The physical principle that every mass attracts every other mass through the force of gravity.

Newton's Universal Law of Gravitation

The gravitational force formula $F_{\text{grav}} = \frac{G Mm}{r^2}$, where $M$ and $m$ are masses, $r$ is the separation between their centres, and $G$ is the gravitational constant.

Gravitational Constant ($G$)

The universal constant of proportionality in Newton's universal law of gravitation.

Weight ($W$)

The gravitational force exerted on an object near a planet, expressed as $F_{\text{grav}} = mg$ or $W = mg$.

Surface Gravitational Field Strength Formula

The formula for gravitational field strength at Earth's surface: $g = \frac{G M_{\text{Earth}}}{R_{\text{Earth}}^2}$.

Earth's Surface Gravitational Field Strength ($g$)

The value of gravitational field strength near Earth's surface, equal to $9.8\,\text{N}\,\text{kg}^{-1} = 9.8\,\text{m}\,\text{s}^{-2}$.

Equivalence of $\text{N}\,\text{kg}^{-1}$ and $\text{m}\,\text{s}^{-2}$

The relationship stating that a gravitational field strength of $1\,\text{N}\,\text{kg}^{-1}$ produces an acceleration of $1\,\text{m}\,\text{s}^{-2}$.

Newton's Third Law of Motion

The law stating that when object A exerts a force on object B, object B exerts an equal and opposite force on object A.

Newton's Third-Law Pairs

Equal and opposite interaction forces that act on different objects, meaning they do not cancel out in a single object's free-body diagram.

Balanced Forces vs. Third-Law Pairs

Balanced forces act on the same object and sum to zero, whereas Newton's 3rd-law pairs act on two separate objects.

Newton's First Law of Motion

The law stating that an object remains at rest or continues moving with constant velocity in a straight line unless acted upon by a non-zero resultant external force.

Uniform Motion

Motion characterised by constant velocity, meaning both speed and direction remain constant.

Translational Equilibrium

The mechanical state where the resultant net force is zero ($F_{\text{net}} = 0$), producing zero acceleration ($a = 0$).

Pressure ($p$)

The force distributed perpendicularly over an area, calculated using $p = \frac{F}{A}$.

Pascal ($\text{Pa}$)

The SI unit of pressure, equivalent to $1\,\text{N}\,\text{m}^{-2}$.

Force from Pressure Formula

The rearranged pressure formula used to compute total force: $F = pA$.

Atmospheric Pressure at Sea Level

The pressure caused by the weight of air above a surface, approximately $1.0 \times 10^5\,\text{Pa}$ at sea level.

System Boundary

The designated boundary chosen to define the specific object or group of objects being analysed.

Free-Body Diagram

A diagram representing only the external forces acting on a chosen system, drawn as arrows labelled with their physical causes.

Normal Contact Force

A support force exerted perpendicular to the surface of contact.

Tension

A pulling force acting along the length of a stretched string, rope, or cable.

Static Friction

A frictional force that prevents relative slipping between surfaces and adjusts up to a limiting maximum value.

Dynamic Friction

A frictional force that opposes relative sliding motion between surfaces in contact.

Buoyancy (Upthrust)

An upward force exerted on an object by a surrounding fluid.

Drag

A resistive force that opposes the motion of an object travelling through a fluid.

Parallel Component of Weight

The component of weight directed parallel to an inclined slope of angle $\theta$, given by $W_{\text{parallel}} = mg \sin(\theta)$.

Perpendicular Component of Weight

The component of weight directed perpendicular to an inclined slope of angle $\theta$, given by $W_{\text{perpendicular}} = mg \cos(\theta)$.

Perpendicular Force Components ($F_x$ and $F_y$)

The components of a force $F$ resolved at angle $\theta$ to the horizontal axis: $F_x = F \cos(\theta)$ and $F_y = F \sin(\theta)$.

Scientific Evidence

Data gathered through observations and controlled investigations used to develop scientific explanations.

Reproducibility

The requirement that independent researchers can repeat an investigation's method and obtain compatible results.

Scientific Skepticism

The standard of testing claims through empirical evidence rather than accepting them on authority or plausibility.

Scientific Theory

A well-supported explanatory framework backed by empirical evidence, distinct from a mere guess.

Peer Review

A quality-control process allowing independent scientists to check methods, reasoning, evidence, and conclusions prior to publication.

Research Question

A specific scientific question identifying how changing one quantity affects another.

Independent Variable

The experimental variable that is deliberately changed or manipulated by the investigator.

Dependent Variable

The experimental variable that is measured as the response to changes in the independent variable.

Controlled Variables

Conditions kept strictly constant throughout an investigation to ensure a fair test.

Repeated Trials

Multiple iterations of experimental measurements performed to identify variation and increase confidence in the result.

Raw Data

Direct measurement records collected from instruments prior to data processing or averaging.

Fair Test

An experimental procedure that changes the independent variable systematically while keeping all other relevant conditions constant.

Analogue Instrument Uncertainty

Uncertainty estimated from the smallest scale division, often about half a division when judging readings between marks.

Digital Instrument Uncertainty

Uncertainty determined by the last displayed digit or by stated instrument specifications.

Measurement Best Estimate Representation

The standard reporting format for a measurement alongside its absolute uncertainty: $x \pm \Delta x$.

Decimal Place Consistency

The reporting convention requiring that the absolute uncertainty and best estimate be reported to consistent decimal places.

Absolute Uncertainty Propagation for Sums and Differences

The rule stating that absolute uncertainties are added together: $\Delta z = \Delta x + \Delta y$ for $z = x \pm y$.

Fractional Uncertainty

The ratio of the absolute uncertainty to the best estimate: $\frac{\Delta x}{x}$.

Percentage Uncertainty

The fractional uncertainty expressed as a percentage: $\text{percentage uncertainty} = \left(\frac{\Delta x}{x}\right) \times 100\%$.

Fractional Uncertainty Propagation

The method of propagating measurement uncertainties for products, quotients, and powers by using fractional uncertainties.

Arithmetic Mean ($\bar{x}$)

The central average of $n$ measurements calculated using $x_{\text{av}} = \bar{x} = \frac{1}{n}\sum x_i$.

Range Method

A technique to estimate spread in repeated trials using half the total range: $\frac{\text{range}}{2} = \frac{\max(x_i) - \min(x_i)}{2}$.

Sample Standard Deviation ($\sigma$)

A statistical measure of spread for a sample, defined by $\sigma = \sqrt{\frac{1}{n-1}\sum (\bar{x} - x_i)^2}$.

Standard Deviation of the Mean ($\sigma_{\text{av}}$)

The uncertainty associated with the calculated mean, given by $\sigma_{\text{av}} = \frac{\sigma}{\sqrt{n}}$.

Direct Proportionality

A relationship of the form $y \propto x$ that produces a straight-line graph passing through the origin.

Inverse Proportionality

A relationship of the form $y \propto \frac{1}{x}$, which produces a straight line when plotting $y$ against $\frac{1}{x}$.

Linear Model

A mathematical model written as $y = mx + c$, where $m$ is the gradient and $c$ is the intercept.

Square-Root Model

A mathematical relationship of the form $y = A\sqrt{x}$, linearised by plotting $y$ against $\sqrt{x}$.

Model Parameters

Fitted constants, such as $A$, $m$, and $c$, that describe a functional mathematical relationship and may carry units.

Error Bars

Graphical lines added to plotted data points to represent the uncertainty window associated with each measurement.

Residuals

The differences between measured values and values predicted by a fitted model; systematic patterns in residuals reveal model inadequacy.

Coefficient of Determination ($R^2$)

A statistical value indicating how closely data follow a fitted model, though a high value does not prove causation or physical correctness.

Pressure at Depth Model

A linear model given by $p = Ad + B$, where $d$ is depth, $A$ is the pressure change rate with depth, and $B$ is surface reference pressure.

Kinematic Distance Model from Rest

The kinematic relation for distance travelled under constant acceleration from rest: $d = \frac{1}{2}at^2$.

Fall Time from Rest Formula

The rearranged kinematic relation for travel time under constant acceleration from rest: $t = \sqrt{\frac{2d}{a}}$, having form $t = A\sqrt{d}$ where $A = \sqrt{\frac{2}{a}}$.

Kinematic Time-Distance Ratio

The relation comparing travel times across two distances under identical constant acceleration: $\frac{t_2}{t_1} = \sqrt{\frac{d_2}{d_1}}$.

Precision

A measure of how closely repeated measurements of the same quantity agree with one another.

Accuracy

A measure of how close an experimental measurement is to the true or accepted reference value.

Uncertainty Window

The range of plausible values defined by a measurement and its absolute uncertainty, extending from approximately $x - \Delta x$ to $x + \Delta x$.

Consistency of Values

The condition where two values agree because their uncertainty windows overlap or their difference is compatible with combined uncertainty.

Random Errors

Unpredictable fluctuations that vary between trials and can often be reduced by repeating measurements and calculating a mean.

Systematic Errors

Flaws that shift experimental measurements in a consistent direction and cannot be eliminated by averaging.

Calibration

The process of comparing a measuring instrument against a known standard to detect and correct systematic errors.