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Physics relies on standardized units to measure and describe the world around us. The provides seven base units from which all other units are derived, ensuring consistency in scientific communication worldwide.

combine base units to measure complex phenomena like and . allow for easy conversion between units of different scales, from tiny nanometers to massive terabytes, making calculations and comparisons simpler across various fields of study.

Units and Standards in Physics

Base units in physics measurements

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  • SI (Système International) international system of units used in physics and other sciences provides a standardized set of units for consistent measurements worldwide
  • SI base units are the fundamental units that define the SI system all other units can be derived from these base units
  • The seven SI base units:
    • (m) measures length
    • (kg) measures mass
    • (s) measures time
    • (A) measures electric current
    • (K) measures temperature
    • (mol) measures amount of substance
    • (cd) measures luminous intensity
  • Using SI base units ensures clarity, consistency, and reproducibility in scientific communication and research allows for easy comparison of results across different studies and laboratories
  • Each SI corresponds to a , which is a fundamental physical property that cannot be defined in terms of other quantities

Construction of derived units

  • are formed by combining SI base units through multiplication or division allows for the measurement and description of complex physical quantities using the fundamental SI base units
  • Examples of derived units:
    • : square meter (m2m^2) formed by multiplying length (m) by length (m) used to measure the surface area of objects
    • : cubic meter (m3m^3) formed by multiplying length (m) by length (m) by length (m) used to measure the space occupied by objects
    • Velocity: meter per (m/s) formed by dividing length (m) by time (s) used to measure the speed and direction of motion
    • : meter per second squared (m/s2m/s^2) formed by dividing velocity (m/s) by time (s) used to measure the rate of change in velocity
    • : (N) formed by multiplying mass (kg) by acceleration (m/s2m/s^2) used to measure the push or pull on an object
    • Energy: (J) formed by multiplying force (N) by distance (m) used to measure the capacity to do work or cause change
  • Constructing derived units allows for a wide range of physical phenomena to be quantified and analyzed using a consistent set of base units
  • can be used to verify the correctness of derived units and equations by ensuring that the dimensions on both sides match

Metric unit conversion techniques

  • Metric prefixes indicate multiples or fractions of each prefix represents a specific scaling factor, which is a power of 10
  • Common metric prefixes and their scaling factors:
    • Tera (T): 101210^{12} (trillion) used for very large quantities (terabyte of data storage)
    • Giga (G): 10910^9 (billion) used for large quantities (gigawatt of power generation)
    • Mega (M): 10610^6 (million) used for moderately large quantities (megahertz of processor speed)
    • Kilo (k): 10310^3 (thousand) used for intermediate quantities (kilometer of distance)
    • Centi (c): 10−210^{-2} (hundredth) used for small quantities (centimeter of length)
    • Milli (m): 10−310^{-3} (thousandth) used for very small quantities (milligram of mass)
    • Micro (μ\mu): 10−610^{-6} (millionth) used for microscopic quantities (micrometer of wavelength)
    • Nano (n): 10−910^{-9} (billionth) used for nanoscale quantities (nanometer of size)
  • To convert between metric units:
    1. Identify the original unit and the target unit
    2. Determine the scaling factor between the units (power of 10)
    3. Multiply or divide the given value by the scaling factor
  • Example: Converting 5 kilometers to meters
    • 1 kilometer = 10310^3 meters
    • 5 kilometers = 5×1035 \times 10^3 meters = 5000 meters
  • Example: Converting 3200 milligrams to grams
    • 1 gram = 10310^3 milligrams
    • 3200 milligrams = 3200÷1033200 \div 10^3 grams = 3.2 grams
  • When converting, ensure the original and target units represent the same (length, mass, time) to maintain
  • is essential for comparing measurements in different systems or scales

Measurement and Representation in Physics

  • is used to express very large or very small numbers in a compact form, making calculations and comparisons easier
  • indicate the precision of a measurement, reflecting the number of reliably known digits
  • is inherent in all physical measurements and should be reported along with the measured value to indicate the range of possible true values

Key Terms to Review (48)

Acceleration: Acceleration is the rate of change of velocity with respect to time. It represents the change in an object's speed or direction over a given time interval, and is a vector quantity that has both magnitude and direction.
Action-at-a-distance force: An action-at-a-distance force is a force exerted by an object on another object that is not in physical contact with it, acting over a distance through space. Examples include gravitational, electromagnetic, and nuclear forces.
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 used to measure the rate of electric charge flow or the strength of an electric current.
Area: Area is a measure of the size or extent of a two-dimensional surface, typically expressed in square units. It is a fundamental concept in physics, geometry, and various other fields, as it quantifies the space occupied by an object or the region within a closed boundary.
Base quantities: Base quantities are fundamental physical quantities in a system of units that are defined independently of other quantities. Examples include length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.
Base Quantity: A base quantity is a fundamental physical quantity that is defined independently and is not derived from other quantities. Base quantities serve as the building blocks for other measurements and are essential in the establishment of a coherent system of units. They provide a standardized reference to describe physical phenomena in a consistent way.
Base unit: A base unit is a fundamental unit of measurement defined by a physical standard, from which other units are derived. Examples include the meter for length and the kilogram for mass.
Candela: The candela (cd) is the base unit of luminous intensity in the International System of Units (SI). It is a measure of the amount of light emitted in a particular direction, and is a fundamental unit used to quantify the brightness or luminous power of a light source.
Centi-: The prefix 'centi-' is a metric system prefix that denotes one-hundredth (1/100) of a unit. It is commonly used in the context of units and standards, as well as unit conversion, to represent a fraction of a larger unit.
Derived quantity: A derived quantity is a physical quantity that is defined in terms of base quantities through multiplication or division. Examples include velocity, acceleration, and force.
Derived units: Derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). These units are used to express physical quantities that cannot be described by a single base unit.
Derived Units: Derived units are units that are created by combining the base units of a measurement system, such as the International System of Units (SI), to express more complex physical quantities. These derived units are essential for describing and quantifying various physical phenomena that cannot be adequately represented by the base units alone.
Dimensional Analysis: Dimensional analysis is a problem-solving technique that uses the relationships between the dimensions of physical quantities to simplify calculations, check the validity of equations, and convert between different units of measurement. It is a fundamental tool in physics that helps ensure the consistency and dimensionality of physical expressions.
Dimensional Consistency: Dimensional consistency is the principle that the dimensions or units of all terms in an equation or expression must be consistent and compatible with one another. It ensures that the overall expression has the correct physical dimensions, which is crucial for the equation to be meaningful and valid.
Energy: Energy is the fundamental quantity that describes the ability to do work or cause change. It is the driving force behind all physical and chemical processes in the universe, from the smallest subatomic interactions to the largest-scale cosmic events. Energy can take many forms, such as kinetic, potential, thermal, electrical, and more, and it is conserved in the sense that it cannot be created or destroyed, only transformed from one type to another.
English units: English units are a system of measurement used primarily in the United States, which includes units such as inches, feet, pounds, and gallons. These units are not based on the metric system and have unique conversion factors.
Force: Force is a vector quantity that represents the interaction between two objects, causing a change in the motion or shape of the objects. It is the fundamental concept that underlies many of the physical principles studied in college physics, including Newton's laws of motion, work, energy, and more.
Giga-: The prefix 'giga-' is a unit prefix in the metric system that denotes a factor of one billion (1,000,000,000 or 10^9). It is used to indicate extremely large quantities or measurements, particularly in the context of scientific and technological applications.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It represents the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
Joule: The joule (J) is the standard unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter.
Kelvin: Kelvin is the base unit of temperature in the International System of Units (SI), named after the British mathematician and physicist William Thomson, 1st Baron Kelvin. It is one of the seven base units in the SI system and is used to measure the absolute temperature of a system, providing a scale that is directly related to the fundamental properties of matter and energy.
Kepler’s second law: Kepler's second law, also known as the law of equal areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun.
Kilo-: The prefix 'kilo-' is a unit prefix in the metric system that denotes a factor of 1,000. It is used to express large quantities or measurements in the context of units and standards, unit conversion, and dimensional analysis.
Kilogram: A kilogram is the base unit of mass in the International System of Units (SI). It is defined by the mass of the International Prototype Kilogram, a platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures.
Kilogram: The kilogram is the base unit of mass in the International System of Units (SI). It is the only SI unit that is still defined by a physical object, rather than a fundamental physical constant. The kilogram is a crucial concept in physics, as it is used to quantify the amount of matter in an object and is a key component in the study of mechanics, thermodynamics, and other areas of physics.
Measurement Uncertainty: Measurement uncertainty is the range of values within which the true value of a measurement is expected to lie. It quantifies the precision and accuracy of a measurement, accounting for various sources of error and variability in the measurement process.
Mega-: The prefix 'mega-' is a unit prefix in the International System of Units (SI) that denotes a factor of one million (10^6) or 1,000,000. It is used to express very large quantities or measurements in the context of physics, chemistry, and other scientific disciplines.
Meter: A meter is the base 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 Prefixes: Metric prefixes are a system of unit prefixes that are used to form decimal multiples and submultiples of the International System of Units (SI). These prefixes are used to create new units by multiplying or dividing the base unit by a specific power of ten, allowing for the expression of very large or very small quantities in a concise manner.
Metric system: The metric system is an international decimalized system of measurement based on the meter, kilogram, and second. It is widely used in science and engineering for accuracy and consistency.
Micro-: The prefix 'micro-' refers to something that is extremely small or minute in size. It is commonly used in scientific and technical contexts to denote measurements or quantities that are on a microscopic scale, often associated with the study of small-scale phenomena or the use of specialized equipment and techniques to observe and analyze such small-scale systems.
Milli-: Milli- is a metric prefix that denotes one-thousandth (1/1,000) of the base unit. It is used to express very small quantities or measurements in the context of the metric system. The prefix 'milli-' is derived from the Latin word 'mille' meaning 'thousand'.
Mole: The mole is the SI unit for the amount of a substance, and it is used to measure the number of particles, such as atoms, molecules, or ions, in a given sample. It is a fundamental unit in chemistry that allows for the quantification of chemical reactions and the composition of substances.
Nano-: The prefix 'nano-' is a unit prefix in the metric system that denotes a factor of one-billionth (10^-9). It is commonly used to describe extremely small measurements or quantities, particularly in the fields of physics, chemistry, and materials science.
Newton: Newton is the standard unit of force in the International System of Units (SI), named after the renowned English physicist and mathematician, Sir Isaac Newton. It is a fundamental unit that is essential in understanding and describing the behavior of objects under the influence of various forces, as well as in the study of mechanics, dynamics, and other related areas of physics.
Physical quantity: A physical quantity is a property of a material or system that can be quantified by measurement. Examples include length, mass, time, and electric current.
Scientific Notation: Scientific notation is a way to express very large or very small numbers in a compact form, typically written as a product of a number between 1 and 10 and a power of 10. This notation makes it easier to handle calculations involving extreme values, which are common in fields that deal with the vast scales of physics and measurements. It also aids in standardizing units and simplifies the process of converting between them, while ensuring that significant figures are maintained in calculations.
Second: The second is the SI unit of time, defined as the duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. It is a fundamental unit in physics and essential for precise measurements.
Second: The second is the base unit of time in the International System of Units (SI). It is 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. The second is a fundamental unit that is essential for measuring and understanding various physical phenomena across the field of physics.
SI system: The SI system, or International System of Units, is a globally accepted system of measurement that provides a standardized way to express physical quantities. It includes a set of base units such as the meter for length, kilogram for mass, and second for time, allowing scientists and engineers to communicate measurements clearly and consistently across different fields and countries.
SI units: SI units are the internationally accepted system of measurement used in science and engineering. They provide a standardized way to quantify physical quantities.
Significant figures: Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, zeroes between significant digits, and trailing zeroes in a decimal number. They indicate the accuracy of measurements and calculations.
Significant Figures: Significant figures, also known as significant digits, refer to the meaningful digits in a measurement or calculation that carry weight and convey the precision of the data. They are essential in expressing the accuracy and reliability of numerical values in the context of physics and other scientific disciplines.
Tera-: The prefix 'tera-' is a unit prefix in the metric system that represents a factor of one trillion (1,000,000,000,000 or 10^12). It is used to denote multiples of a base unit, such as length, mass, or time, by a factor of one trillion.
Unit Conversion: Unit conversion is the process of changing the unit of a quantity to a different unit that represents the same value. It is a fundamental concept in physics and other scientific disciplines, allowing for the consistent and accurate measurement and comparison of physical quantities.
Velocity: Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the speed and the direction of an object's motion, making it a more complete description of an object's movement compared to just speed alone.
Volume: Volume is a measure of the three-dimensional space occupied by an object or substance. It is a fundamental physical quantity that describes the amount of space a particular body or material takes up.
Volume strain: Volume strain is the change in volume of a material divided by its original volume when subjected to stress. It is a dimensionless quantity indicating how much a material deforms under pressure or external forces.
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Glossary
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1.3 Unit Conversion