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Question

Plane angle is obtained by dividing arc length by radius then it should be a derived quantity but why do we call it as fundamental quantity?

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Solution

Actually radian(of plane angle)) and steredian(of solid angle) were supplementary SI Units Plane angle: radian (rad) and solid angle: steradian (sr)

The radian and steradian were classified as supplementary units.

At the time of the introduction of the International System, the question of the nature of these supplementary units was left open. Considering that plane angle is generally expressed as the ratio between two lengths and solid angle as the ratio between an area and the square or a length, it was specified that in the International System the quantities plane angle and solid angle should be considered as dimensionless derived quantities. Therefore, the supplementary units radian and steradian are to be regarded as dimensionless derived units which may be used or omitted in the expressions for derived units.

Since October , 1995, the class of supplementary units as a separate class in the SI has been removed. Thus the SI now consists of only two classes of units: base units and derived units, with the radian and steradian, which were the two supplementary units, moved into the class of SI derived units.
So 7 fundamental quantities are length,mass ,time,electric current,Thermodynamic temperature,amount of substance,luminous intensity.

Hope you understood.


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