why plane angle and solid angle considered as supplementary base units
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Why is a plane angle called a supplementary unit?
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Henry Alman, BSc Physics, Imperial College London (2019)
Answered Aug 9, 2018 · Author has 431answers and 95.6k answer views
(Thanks to Sonam Shrish Magar for requesting this answer.)
They’re not! Firstly, the plane angle is a quantity, not a unit. It is measured in units, e.g. radians.
However, even radians and steradians are not “supplementary units.” In 1995, the “supplementary unit” was removed as a class of unit from the SI system.
They were instead grouped with the “derived units”, which is essentially everything that’s not one of the seven “base units” (metre, kilogram, second, ampere, kelvin, candela, mole.) This includes everything from Teslas for magnetic flux density to unnamed things like “metres squared” for area.
I think they may have originally been classed separately just because they were dimensionless units.
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Henry Alman, BSc Physics, Imperial College London (2019)
Answered Aug 9, 2018 · Author has 431answers and 95.6k answer views
(Thanks to Sonam Shrish Magar for requesting this answer.)
They’re not! Firstly, the plane angle is a quantity, not a unit. It is measured in units, e.g. radians.
However, even radians and steradians are not “supplementary units.” In 1995, the “supplementary unit” was removed as a class of unit from the SI system.
They were instead grouped with the “derived units”, which is essentially everything that’s not one of the seven “base units” (metre, kilogram, second, ampere, kelvin, candela, mole.) This includes everything from Teslas for magnetic flux density to unnamed things like “metres squared” for area.
I think they may have originally been classed separately just because they were dimensionless units.
virag7:
but in our textbook it is given that these two are supplementary quantitues.
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A solid angle is an angle used in the analysis of 3 dimensional space. For example, when calculating the intensity of radiation on a given surface, one must consider the solid angle subtended by the source radiation. Thus, it not only has to account for the angle between the x and y axes, but it must also account for the angle created between the plane within which the x and y axes exist and the perpendicular z axis. So there will be two angles. Distance will also factor in significantly for the solid angle, as this is how one may account, mathematically speaking, for being able to cover the moon with a baseball. So proximity between the objects in a solid angle is also of major importance.
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