1.1.1

Use of SI Units

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SI Base Units

SI base units are the standard units used to describe physical quantities in physics. They are:

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Metre (m)

  • The SI unit for distance (length).
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Kilogram (kg)

  • The SI unit for mass.
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Second (s)

  • The SI unit for time.
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Ampere (A)

  • The SI unit for electric current.
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Kelvin (K)

  • The SI unit for temperature.
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Mole (mol)

  • The SI unit for chemical mass.
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Candela (cd)

  • The SI unit for luminous intensity.

Combining SI Units

SI base units can be combined to form lots of other useful SI units:

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Hertz (Hz)

  • The SI unit for frequency.
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Newton (N)

  • The SI unit for force.
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Joule (J)

  • The SI unit for energy.
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Watt (W)

  • The SI unit for power.
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Pascal (Pa)

  • The SI unit for pressure.
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Coulomb (C)

  • The SI unit for electric charge.
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Volt (V)

  • The SI unit for electric potential difference.
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Ohm (Ω.)

  • The SI unit for electrical resistance.
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Tesla (T)

  • The SI unit for magnetic flux density.

Celsius (°C)

  • Degrees Celsius are derived from the base SI unit for temperature (Kelvin).
  • To convert between Kelvin and °C use the following equation:
    • °C = K - 273.

Homogeneous Equations

We can use the SI base units to check the equations that relate different physical quantities.

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Homogeneous equations

  • In maths, we are used to the left-hand side of equations equalling the right-hand side.
  • When the numbers involved have units, the units of the left-hand side must be of the same type as the units of the right-hand side.
  • This is what is meant by a homogeneous equation.
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Homogeneous equations

  • For example, 5 m + 5 m = 10 g doesn't make any physical sense, though the numbers add up correctly.
  • However, 10 km = 10,000 m does make sense, as both kilometres and meters are units of distance.
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Equation for speed

  • We know that the SI base unit for time is the second and for distance is the metre.
  • So the SI derived unit for speed is metres per second.
  • Writing this in equation form:
    • speed=distancetimemetres per second=metresseconds\text{speed} = \frac{\text{distance}}{\text{time}}\rightarrow \text{metres per second} = \frac{\text{metres}}{\text{seconds}}
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Derived units

  • We can use the fact that equations are homogeneous to work out units for physical quantities in terms of the SI base units.
  • For example, Newton's second law or F=maF=ma has dimensions:
    • Newtons=kilograms×metres per second squared\text{Newtons} = \text{kilograms}\times \text{metres per second squared}
  • So a force of 10 N is equivalent to 10 kgms-2.

Jump to other topics

1Physical Quantities & Units

2Measurement Techniques

3Kinematics

4Dynamics

5Gravitational Fields

6Deformation of Solids

7Thermal Physics

8Oscillations

9Communication

10Electric Fields

11Current Electricity

12Magnetic Fields

13Modern Physics

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