Question

Hola !! Physics Experts !
Explain the Supplementary physical quantity and its types [plane angle, solid angle] with practical examples

Proper Explanation needed!!
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Answer 1

Definition :

Supplementary units are the dimensionless units that are used along with the base units to form derived units in the International system. Supplementary quantities are geometrical quantities of circle and sphere.

Length, Mass, Time, Thermodynamic, Temperature, Strength of Electrical Current, Amount of substance and Luminous Intensity. Supplementary Physical Quantities.

Types :

Plane Angle :

A plane angle is well known: one full revolution is 360° or 2π radians. The solid angle expands this concept over the surface of a sphere. The solid angle , is seen from the centre of a sphere, includes a given area on the surface of that sphere. The value of the solid angle is numerically equal to the size of that area divided by the square of the radius of the sphere.

Solid Angle :

A solid angle is a 3D angular volume that is defined analogously to the definition of a plane angle in two dimensions. A solid angle, ω, made up of all the lines from a closed curve meeting at a vertex, is defined by the surface area of a sphere subtended by the lines and by the radius of that sphere.

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Answer 2

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Definition:-

Supplementary quantities are geometrical quantities of circle and sphere. Supplementary are the units not still classified either as base or derived. There are two supplementary units of two purely" geometrical physical quantities" and they're;

•Physical quantities:-  

→ Plane angle and solid angle.

•Units:-  

→ Radian and steradian respectively.

PLANE ANGLE:-

A plane angle is defined by the arc length of a circle subtended by the lines and by the radius of that circle. The dimensionless unit of plane angle is the radian, with 2π radians in a full circle.

                                                (OR)

A plane angle is made between the crossing of two straight lines or the junction of two planes. The SI Unit of plane angle is radian, and it is expressed as 'rad', radians are used for measuring angles.

SOLID ANGLE:-

Solid angle is an angle made by three or more planes joining at a common point and identified as 'angle formed at  the cone's vertex. The solid angle's SI unit is steradian, and it is expressed as 'sr'. Solid angle is utilized to estimate the amount of the field view from some special point that an object covers.

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