1.2 Physical Quantities and Units
4 min read•june 18, 2024
Measuring and converting is crucial in physics. From meters to feet, kilograms to pounds, we use different systems to quantify our world. Understanding these conversions helps us communicate scientific findings across cultures and disciplines.
Extreme measurements require special notation. Metric prefixes like and help us express very large or small quantities. Scientific notation and ensure in our calculations, allowing us to tackle complex problems with confidence.
Fundamental Units and Measurements
Conversion of measurement systems
Top images from around the web for Conversion of measurement systems
1.1 The Scope and Scale of Physics | University Physics Volume 1 View original
Is this image relevant?
Table on Derived quantities and their SI units | Measurements View original
Is this image relevant?
Units | Boundless Physics View original
Is this image relevant?
1.1 The Scope and Scale of Physics | University Physics Volume 1 View original
Is this image relevant?
Table on Derived quantities and their SI units | Measurements View original
Is this image relevant?
1 of 3
Top images from around the web for Conversion of measurement systems
1.1 The Scope and Scale of Physics | University Physics Volume 1 View original
Is this image relevant?
Table on Derived quantities and their SI units | Measurements View original
Is this image relevant?
Units | Boundless Physics View original
Is this image relevant?
1.1 The Scope and Scale of Physics | University Physics Volume 1 View original
Is this image relevant?
Table on Derived quantities and their SI units | Measurements View original
Is this image relevant?
1 of 3
- Length
- SI unit: (m) is the standard unit of length in the
- English unit: (ft) is a common unit of length in the US customary system
- Conversion: 1 m equals 3.28084 ft, allowing for easy conversion between the two systems (ruler, measuring tape)
- Mass
- SI unit: (kg) is the base unit of mass in the metric system
- English unit: (lb) is a unit of mass in the US customary system
- Conversion: 1 kg equals 2.20462 lb, enabling conversion between metric and US customary units (scale, balance)
- Time
- SI unit: (s) is the base unit of time in both SI and English systems
- English unit: (s) is used in both systems, ensuring consistency
- Conversion: 1 s equals 1 s, as the units are identical (clock, stopwatch)
- Temperature
- SI unit: Kelvin (K) is the base unit of temperature in the metric system, with zero K representing absolute zero
- English unit: (°F) is a temperature scale used in the US, with 32°F as the freezing point of water
- Conversion: temperature in K equals , allowing for temperature conversion (thermometer, thermocouple)
- Force
- SI unit: (N) is the derived unit of force in the metric system, defined as the force needed to accelerate 1 kg by 1 m/s²
- English unit: (lbf) is a unit of force in the US customary system, equal to the gravitational force exerted on a mass of 1 lb
- Conversion: 1 N equals 0.224809 lbf, facilitating force conversion between the two systems (spring scale, force gauge)
Expression of extreme measurements
- Metric prefixes
- Giga (G): represents or 1 billion times the base unit (gigabyte, gigawatt)
- (M): represents or 1 million times the base unit (megabyte, megahertz)
- (k): represents or 1 thousand times the base unit (kilometer, )
- (c): represents or one-hundredth of the base unit (centimeter, centiliter)
- (m): represents or one-thousandth of the base unit (millimeter, milliliter)
- (): represents or one-millionth of the base unit (micrometer, microfarad)
- Nano (n): represents or one-billionth of the base unit (nanometer, nanosecond)
- Scientific notation
- Expresses numbers as a product of a number between 1 and 10 and a power of 10, simplifying the representation of very large or small quantities
- Example: Avogadro's number, , represents the number of particles in one mole of a substance
- Useful for representing quantities such as atomic sizes (angstroms) or astronomical distances (light-years) concisely
- Significant figures
- Indicate the precision of a measurement by showing the number of digits that are reliably known
- Help in determining the of calculations involving measured quantities
Fundamental SI units
- Length: meter (m)
- Defined as the distance traveled by light in a vacuum in seconds, ensuring a precise and universally accessible standard
- Practical realizations include laser interferometry and atomic transition frequencies (ruler, measuring tape, laser rangefinder)
- Mass: kilogram (kg)
- Defined by the international prototype kilogram, a cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures in France, ensuring a consistent global standard
- The kilogram is the only SI base unit still defined by a physical artifact (balance, scale)
- Time: second (s)
- Defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom, providing an extremely precise and stable time standard
- Atomic clocks use this definition to maintain accurate time (clock, stopwatch, GPS)
- Electric current: (A)
- Defined as the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in a vacuum, would produce a force equal to newton per meter of length between the conductors
- This definition relates electric current to the of length, mass, and time (ammeter, multimeter)
Measurement and Analysis
- and
- Base units (e.g., meter, kilogram, second) are the fundamental units in the (SI)
- (e.g., newton, joule, watt) are formed by combining base units according to the algebraic relations of the corresponding quantities
-
- A method for analyzing the relationships between different physical quantities by identifying their base dimensions
- Useful for checking the consistency of equations and converting between different units
- Precision and accuracy
- Precision refers to the reproducibility of measurements and is related to random errors
- Accuracy describes how close a measurement is to the true value and is affected by systematic errors
- Both concepts are crucial for evaluating the quality of scientific measurements and experiments
Key Terms to Review (39)
Accuracy: Accuracy refers to the closeness of a measurement or calculation to the true or accepted value. It is a measure of how precise and reliable a result is, and it is a critical concept in the fields of physics, engineering, and scientific research.
Ampere: An ampere (A) is the unit of electric current in the International System of Units (SI). It represents the flow of one coulomb of charge per second.
Ampere: The ampere (symbol: A) is the base unit of electric current in the International System of Units (SI). It is defined as the constant flow of one coulomb of electrical charge per second, and it is a fundamental quantity used to describe the movement of electric charge.
Angstrom: An angstrom is a unit of length used to measure extremely small distances, particularly in the fields of atomic, molecular, and optical physics. It is a widely used unit in the study of physical quantities and their units.
Base units: Base units are the fundamental units of measurement that define physical quantities in the International System of Units (SI). These units serve as the building blocks for all other derived units, allowing scientists and researchers to quantify and communicate measurements consistently across different fields. The seven base units correspond to specific physical quantities, providing a standardized way to express measurements globally.
Centi: Centi is a metric prefix that denotes one-hundredth (1/100) of a given unit. It is commonly used to represent smaller measurements and quantities in various scientific and everyday applications.
Conversion factor: A conversion factor is a ratio used to convert one unit of measurement into another. It expresses the equivalence between two different units.
Degree Fahrenheit: The degree Fahrenheit (°F) is a unit of temperature used primarily in the United States. It is based on a scale where the freezing point of water is 32°F and the boiling point is 212°F under standard atmospheric conditions.
Derived units: Derived units are units of measurement obtained by combining the base units according to the physical relationships between quantities. Examples include meters per second (m/s) for velocity and newtons (N) for force.
Derived Units: Derived units are units that are defined by combining or manipulating the base units of a measurement system. They are used to quantify physical quantities that cannot be directly measured using the base units alone, such as area, volume, and speed.
Dimensional analysis: Dimensional analysis is a mathematical technique used to convert one set of units to another by analyzing the dimensions of the physical quantities involved. This method relies on the principle that equations must be dimensionally consistent, allowing for the verification of formulas and calculations involving physical quantities. It plays a vital role in ensuring accuracy in measurements and simplifying complex calculations by focusing on the dimensions of the quantities.
English units: English units are a system of measurement commonly used in the United States, including units such as inches, feet, pounds, and gallons. They are distinct from the metric system and often require conversion for scientific calculations.
Fahrenheit: Fahrenheit is a temperature scale that measures the degree of heat or cold. It is commonly used in the United States and a few other countries, with the freezing point of water at 32°F and the boiling point at 212°F under standard atmospheric pressure.
Foot: A foot is a unit of length in the imperial and US customary measurement systems. It is commonly used to measure the dimensions of physical objects and distances. The foot is a fundamental unit in the study of physical quantities and their associated units.
Fundamental units: Fundamental units are the basic units of measurement defined by a standard, from which all other units are derived. Examples include meters for length, kilograms for mass, and seconds for time.
Giga: Giga is a prefix used in the International System of Units (SI) to denote a factor of one billion (1,000,000,000 or 10^9). It is commonly used to quantify large physical quantities in various scientific and technological fields.
International System of Units: The International System of Units (SI) is a standardized system used globally for measuring physical quantities. It provides a consistent framework for scientists and engineers to communicate measurements, ensuring that they can be understood universally. The SI system is built on seven base units, which can be combined to derive other units, promoting clarity and precision in scientific work.
Kilo: Kilo is a prefix used in the International System of Units (SI) to denote a factor of one thousand. It is commonly used to quantify various physical quantities and units, providing a standardized way to express large or small measurements.
Kilogram: A kilogram is the base unit of mass in the International System of Units (SI). It is defined by taking the fixed numerical value of the Planck constant, $h$, to be $6.62607015 \times 10^{-34}$ when expressed in units of $\text{kg} \cdot \text{m}^2 / \text{s}$.
Kilogram: The kilogram is the base unit of mass in the International System of Units (SI). It is a fundamental physical quantity that is used to measure the amount of matter in an object, and it serves as the foundation for understanding concepts related to physical quantities, accuracy, precision, and Newton's laws of motion.
Light-Year: A light-year is a unit of distance used in astronomy to measure the vast distances between celestial objects. It is defined as the distance that light travels in a vacuum in one year, which is approximately 9.46 trillion kilometers or 5.88 trillion miles.
Mega: Mega is a metric prefix used to denote a factor of one million, or 10^6. This term is often used in various scientific fields to simplify the representation of large quantities, making it easier to understand and communicate measurements. In the context of physical quantities and units, mega plays an important role in converting and expressing values, especially when dealing with large-scale measurements like energy, distance, and data.
Meter: A meter is the fundamental unit of length in the International System of Units (SI). It is defined as the distance light travels in a vacuum in 1/299,792,458 seconds.
Metric system: The metric system is a decimal-based system of measurement used internationally for scientific and everyday measurements. Its units include meters for length, kilograms for mass, and seconds for time.
Micro: Micro is a prefix used in the metric system to denote one-millionth (1/1,000,000) of a base unit. It is commonly used in the context of physical quantities and units to represent extremely small measurements or values.
Milli: Milli is a metric prefix that denotes a factor of one thousandth, or 1/1000, of a given unit. It is commonly represented by the symbol 'm' and is used in the International System of Units (SI) to simplify the expression of very small quantities. By using this prefix, measurements can be expressed in a more manageable way, allowing for clearer communication and understanding of physical quantities.
Nano: Nano is a prefix used to denote one-billionth (1/1,000,000,000) of a specific unit. In the context of physical quantities and units, the term 'nano' is used to describe extremely small measurements and scales, often in the realm of nanoscience and nanotechnology.
Newton: The newton (N) is the standard unit of force in the International System of Units (SI). It is named after the famous English physicist Sir Isaac Newton, who made significant contributions to the understanding of the concept of force and its role in the laws of motion.
Newton’s second law of motion: Newton’s second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it is represented as $F = ma$, where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration.
Order of magnitude: An order of magnitude is a class in a system of classification determined by size, typically measured in powers of ten. It is used to compare quantities by their relative scale.
Physical quantity: A physical quantity is a property of a material or system that can be quantified by measurement. Examples include length, time, mass, and temperature.
Pound: The pound is a unit of mass and weight in the Imperial and United States customary systems of measurement. It is commonly used to measure the mass or weight of physical objects, especially in the context of everyday items and commodities.
Pound-Force: Pound-force (lbf) is a unit of force in the United States Customary System of measurement. It is the force required to accelerate a mass of one pound by an acceleration of one foot per second squared.
Precision: Precision refers to the consistency and repeatability of measurements, indicating how closely related a series of measurements are to one another. High precision means that repeated measurements yield similar results, regardless of whether those results are close to the true value. This concept is crucial for evaluating physical quantities and units, understanding significant figures, making approximations, and interpreting null measurements.
Second: A second is the base unit of time in the International System of Units (SI). Defined as 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
Second: The second is the base unit of time in the International System of Units (SI). It is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. The second is a fundamental physical quantity that is essential for understanding and measuring various physical phenomena across multiple fields, including physics, chemistry, and engineering.
SI units: SI units (International System of Units) are the standard units of measurement used globally in science and industry. They ensure consistency and accuracy in the representation of physical quantities.
Significant Figures: Significant figures are the digits in a number that carry meaningful information about its precision. They include all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal part. Understanding significant figures is essential when dealing with physical quantities, as it ensures that measurements reflect the accuracy and precision of data collected.
Units: Units are standardized quantities used to measure physical quantities. They provide a reference for expressing and comparing measurements accurately.