Comprehensive Physics Study Guide on Base Units and Derived Quantities

SI Base Quantities and Units

Modern physics relies on a standardized system of measurements known as the International System of Units (SI). There are six primary base quantities documented in this study of physics, each associated with a specific symbol, unit name, and unit symbol. These quantities serve as the foundational building blocks for all other measurements. The first is Mass, denoted by the symbol $m$, with the base unit being the kilogram ($kg$). The second is length, denoted by the symbol $l$ or $z$, with the base unit being the metre ($m$). The third base quantity is Temperature, represented by the symbol $T$, which is measured in the base unit kelvin ($K$). The fourth quantity is Current, denoted by the symbol $I$, measured in the ampere ($A$). It is specifically noted that the symbol for Ampere is a capital letter. The fifth base quantity is Time, denoted by the symbol $t$, with the base unit being the second ($s$). Finally, the sixth quantity is the Amount of Substance, signified by the symbol $n$, which is measured in the base unit mole ($mol$).

Understanding Derived Quantities

Derived quantities are physical properties that are calculated or derived from the base units of mass, length, current, and time. For instance, the Area of a circle is calculated using the formula $\text{Area} = \text{pi} \times r^2$, which is derived solely from the base unit of length and measured in metre squared or square metre ($m^2$). Volume, denoted as $V$, is calculated as $m \times m \times m$, resulting in the unit metre cubed or cubic metre ($m^3$), also derived from length. Density, represented by the Greek symbol rho ($\rho$), is the ratio of mass to volume ($\frac{\text{mass}}{\text{volume}}$), making it a quantity derived from mass and length, with the unit kilogram per metre cubed ($kg/m^3$ or $kg \times m^{-3}$).

Mechanical quantities like Velocity and Speed are defined by the ratio of distance to time ($\frac{\text{length}}{\text{time}}$). Consequently, they are derived from length and time and measured in units of metre per second ($m/s$ or $m \times s^{-1}$). Acceleration ($a$) is defined as the change in velocity over time ($\frac{\text{velocity}}{\text{time}}$), making it a quantity derived from length and time squared, measured in metre per second squared ($m/s^2$ or $m \times s^{-2}$). Force ($F$) is calculated as mass multiplied by acceleration ($mass \times acceleration$). It is derived from mass, length, and time, with the unit kilogram metre per second squared or the Newton ($N$), expressed as $kg \times m/s^2$.

Advanced Derived Measurements and Energy

Work and Energy ($W/E$) are derived from mass, length, and time. Work can be expressed using the formula for gravitational potential energy: $m \times g \times \text{delta } h$, where $m$ is mass, $g$ is the gravitational field strength, and $\text{delta } h$ ($\text{Δ}h$) is the change in height. The gravitational field strength is expressed as $\frac{\text{Force}}{\text{mass}}$. The derived unit for Work and Energy is kilogram metre squared per second squared ($kg \times m^2/s^2$), also known as the Joule ($J$). Power ($P$) is the rate at which work is done over time ($Power = \frac{W}{t}$). It is derived from mass, length, and time, with the unit kilogram metre squared per second cubed ($kg \times m^2/s^3$), also known as the Watt ($W$). In the realm of electromagnetism, Charge is defined as the flow of current over time ($Charge = I \times t$). This quantity is derived from the base units of Time and Current.

Mathematical Symbols and Physics Prefixes

In physics notation, several Greek letters and symbols are routinely used to denote mathematical operations or specific states. The symbol Sigma ($\text{Σ}$) represents "the sum of" a set of values. The symbol Delta ($\text{Δ}$) indicates "the change in" a particular quantity. The symbol Theta ($θ$) is used to represent temperature measured specifically in degrees Celsius ($^∘C$). Additionally, scientific notation and prefixes are used to manage different scales of measurement. For example, the prefix "micro" is mathematically defined as $10^{-6}$. Applying a prefix like micro means that a quantity is one million times ($1,000,000$) smaller than another reference unit.

Precision and Significant Figures

Accurate scientific reporting requires the correct use of significant figures (s.f.) to indicate the precision of a measurement. According to the notes dated June 1, 2026, when rounding numbers to three significant figures, specific rules regarding placeholders must be followed. For example, the number $47.28$ rounded to three significant figures becomes $47.3$. The rule states that one should not add a zero as a placeholder when the significant figure falls in a decimal place (e.g., do not write "47.30" if only three figures are significant). Conversely, for large whole numbers, zeros are used as placeholders to maintain the magnitude of the number. For instance, the number $54894$ rounded to three significant figures becomes $54900$. In this case, the zeros are necessary to indicate the value is roughly fifty-four thousand nine hundred, even though only the first three digits are known with precision.