Derived Units in SI Measurements

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Questions and Answers

What is the current definition of a meter based on?

  • The average length of a day
  • The distance traveled by light in a vacuum in 1/299792458 of a second (correct)
  • The length of the Earth’s equator
  • The distance between the North Pole and the equator

Which statement is true about the kilogram's current definition?

  • It relies on Planck’s constant and is expressed in the units of kg m² s⁻¹. (correct)
  • It is based on the mass of one liter of water at boiling point.
  • It is defined using the speed of sound in water.
  • It was initially equivalent to one cubic meter of mercury.

What fixed value is essential in the definition of the ampere?

  • The current through a resistor
  • The charge of the electron (correct)
  • The charge of a proton
  • The voltage measured across a capacitor

The kelvin scale is related to which constant for its definition?

<p>Boltzmann constant (C)</p> Signup and view all the answers

What was the original definition of the second based on?

<p>1/86400 of a solar day (A)</p> Signup and view all the answers

What is the symbol for the derived unit of electrical resistance?

<p>Ω (B)</p> Signup and view all the answers

Which of the following derived units is associated with luminous flux?

<p>lm (D)</p> Signup and view all the answers

How many derived units with special names are there?

<p>22 (A)</p> Signup and view all the answers

What derived unit measures energy?

<p>J (B)</p> Signup and view all the answers

Which of the following is NOT a dimensionless derived unit?

<p>newton (C)</p> Signup and view all the answers

What is the derived unit for electric charge?

<p>C (C)</p> Signup and view all the answers

Which derived unit expresses pressure?

<p>Pa (A)</p> Signup and view all the answers

What derived unit is used to measure frequency?

<p>Hz (D)</p> Signup and view all the answers

What is the symbol for liter?

<p>l (C)</p> Signup and view all the answers

Which of the following is not a permitted non-SI unit?

<p>bar (C)</p> Signup and view all the answers

What quantity does the symbol 'ha' represent?

<p>area (A)</p> Signup and view all the answers

Which of the following non-SI units is used to measure energy?

<p>electronvolt (B)</p> Signup and view all the answers

Which two symbols both represent logarithmic ratios?

<p>Np and dB (C)</p> Signup and view all the answers

What is the quantity associated with the symbol 't'?

<p>mass (A)</p> Signup and view all the answers

Which of the following units represents a plane angle?

<p>° (A)</p> Signup and view all the answers

What unit has an alternative name of 'l' and measures volume?

<p>liter (D)</p> Signup and view all the answers

Which unit for length is no longer permitted in the latest SI brochure?

<p>angstrom (B)</p> Signup and view all the answers

What does the symbol 'au' stand for?

<p>length (A)</p> Signup and view all the answers

What is the symbol for the unit of mass in the SI base units?

<p>kg (C)</p> Signup and view all the answers

Which base unit is used to measure thermodynamic temperature?

<p>K (A)</p> Signup and view all the answers

What property is the second defined based on?

<p>Atomic clock (C)</p> Signup and view all the answers

Which of the following base units measures luminous intensity?

<p>cd (B)</p> Signup and view all the answers

How are the names of the SI base units typically written?

<p>In lowercase letters (B)</p> Signup and view all the answers

Why were the SI base unit definitions re-defined in 2019?

<p>To derive from constant properties of nature (D)</p> Signup and view all the answers

What does the SI unit 'A' stand for?

<p>Ampere (A)</p> Signup and view all the answers

Which unit is used to measure the amount of substance?

<p>mol (C)</p> Signup and view all the answers

What is the symbol for the base unit of length?

<p>m (B)</p> Signup and view all the answers

Which of the following is NOT one of the seven SI base units?

<p>Energy (A)</p> Signup and view all the answers

What is the unit of density?

<p>kg/m3 (B)</p> Signup and view all the answers

Which quantity is represented by the symbol 'V'?

<p>Volume (C)</p> Signup and view all the answers

What does the abbreviation 'm/s' represent?

<p>Meters per second (C)</p> Signup and view all the answers

What is the derived unit for acceleration?

<p>meters per second per second (A)</p> Signup and view all the answers

Which symbol is used for concentration (molarity)?

<p>C (A), M (D)</p> Signup and view all the answers

What defines a derived unit?

<p>A unit created from two or more base units (C)</p> Signup and view all the answers

What is the SI unit for angular velocity?

<p>radians/second (B)</p> Signup and view all the answers

Which of the following represents current density?

<p>A/m2 (C)</p> Signup and view all the answers

What represents the unit for wave number?

<p>m-1 (D)</p> Signup and view all the answers

How can a new derived unit be officially recognized?

<p>By approval from the General Conference on Weights and Measures (A)</p> Signup and view all the answers

Flashcards

Derived Unit

A unit that is derived from one or more base units of measurement.

Named Derived Unit

A unit of measurement that has a specific name and symbol assigned to it, often representing a complex combination of base units.

Unnamed Derived Unit

A unit of measurement expressed as a combination of base units. No specific name or symbol is assigned to it.

Dimensional Analysis

The process of analyzing the dimensional consistency of a physical quantity by expressing it in terms of its fundamental dimensions (length, mass, time, etc.).

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Hertz (Hz)

The SI unit of frequency, representing one cycle per second.

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Newton (N)

The SI unit of force, representing the amount of force needed to accelerate a 1 kg mass at 1 meter per second squared.

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Joule (J)

The SI unit of energy, representing the amount of energy needed to move a 1 kg mass over a distance of 1 meter with a force of 1 Newton.

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Watt (W)

The SI unit of power, representing the rate at which energy is transferred or used.

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Area

The amount of space a two-dimensional object takes up, calculated by multiplying length by width.

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Volume

The amount of space a three-dimensional object takes up, calculated by multiplying length by width by height.

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Density

The ratio of mass to volume, representing how much matter is packed into a given space.

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Concentration (Molarity)

The amount of a substance dissolved in a given volume of solution, often expressed in moles per liter.

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Speed

The rate of change of position over time, often expressed in meters per second.

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Acceleration

The rate of change of speed over time, often expressed in meters per second squared.

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Angular Velocity

The rate of change of angular position (angle) over time, often expressed in radians per second.

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Current Density

The amount of electric current passing through a given cross-sectional area, often expressed in amperes per square meter.

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Wave Number

The reciprocal of wavelength, often expressed in reciprocal meters.

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Specific Volume

The volume occupied by a substance per unit mass, often expressed in cubic meters per kilogram.

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Minute

A unit of time equal to 60 seconds.

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Hour

A unit of time equal to 60 minutes.

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Day

A unit of time equal to 24 hours.

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Astronomical Unit (AU)

A unit of length equal to the average distance between the Earth and the Sun.

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Degree (°)

A unit of plane angle, equal to 1/360th of a full circle.

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Minute (′)

A unit of plane angle, equal to 1/60th of a degree.

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Second (″)

A unit of plane angle, equal to 1/60th of a minute.

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Hectare (ha)

A unit of area equal to 10,000 square meters.

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Liter (l)

A unit of volume equal to one cubic decimeter.

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Tonne (t)

A unit of mass equal to 1000 kilograms.

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Second

Originally defined as 1/86400 of a day, but now based on the frequency of radiation emitted by a cesium-133 atom. This standard ensures a precise and unchanging unit.

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Meter

Initially based on the distance from the equator to the North Pole, the modern meter is defined as the distance light travels in a vacuum in 1/299792458 of a second. This definition connects the meter to the speed of light, a fundamental constant.

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Kilogram

Originally defined as the mass of a liter of water, the kilogram now relies on Planck's constant, a fundamental constant in quantum physics, and the definitions of the meter and second. This definition connects the kilogram to the fundamental laws of nature.

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Ampere

Originally defined by the amount of silver deposited by an electric current, the ampere is now based on the fundamental electric charge of an electron, a constant value. This definition connects the ampere to the building blocks of electric charge.

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Kelvin

Initially defined by the freezing point of water, the Kelvin scale now relies on the Boltzmann constant, a fundamental constant in thermodynamics, and the definitions of the meter, kilogram, and second. This definition connects the Kelvin scale to the fundamental laws of thermal energy.

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What are SI Base Units?

The standard units of measurement in the International System of Units (SI) for seven base quantities. All other SI units are derived from these seven base units.

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What is a Second defined by?

The SI base unit for time, defined using the cesium-133 atom's vibrations.

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How is a Meter defined?

The SI base unit for length, defined using the speed of light in a vacuum.

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What defines a Kilogram?

The SI base unit for mass, defined using Planck's constant, the meter, and the second.

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How is an Ampere defined?

The SI base unit for electric current, defined using the fundamental electric charge of an electron.

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How is a Kelvin defined?

The SI base unit for thermodynamic temperature, defined using the Boltzmann constant.

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What is a Mole?

The SI base unit for amount of substance, defined as the number of particles equal to 6.022 x 10^23.

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What is a Candela?

The SI base unit for luminous intensity, defined as a specific type of light source.

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Study Notes

Derived Units

  • Derived units are combinations of base units
  • Written using lowercase letters
  • Some have special names
  • Symbols for named units start with a capital letter

Examples of Derived Units

  • Watt (W)
  • Hertz (Hz)
  • Coulomb (C)

SI Base Units

  • Time (second, s)
  • Length (meter, m)
  • Mass (kilogram, kg)
  • Electric Current (ampere, A)
  • Temperature (kelvin, K)
  • Amount of substance (mole, mol)
  • Luminous intensity (candela, cd)

More Derived Units

  • Area (square meter, m²)
  • Volume (cubic meter, m³)
  • Density (kilograms per cubic meter, kg/m³)
  • Speed (meters per second, m/s)
  • Acceleration (meters per second squared, m/s²)
  • Pressure (pascal, Pa)
  • Force (newton, N)
  • Energy (joule, J)
  • Frequency (hertz, Hz)
  • Power (watt, W)
  • Voltage (volt, V)
  • Charge (coulomb, C)

Additional Points

  • There are 22 derived units with special names
  • There are more than 100 other derived units, expressed using base units
  • Several SI units that were in the 8th brochure are not in the 9th: bar, mmHg, ångström, gauss
  • Derived units may be based on physical constants
  • The definitions of the SI base units are based on natural phenomena, not physical objects.

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