Confusing Solid And Plane Angles

[Kehsibashok]

Confusing Solid And Plane Angles !

Supplementary Quantities -
1.Solid Angle - Steradian
2.Plane Angle - Radian

Doubts -
1.What Is The Use Of Supplementary Quantities ? Physical Quantities Are Used To Measure For Example .. To Measure

Length - m Current - ampere Etc... What Can I Measure Using Those.. Supplementary Quantities ? So Confusing...

2.What Is Solid Angle ? What Is Plane Angle ?

Kindly Explain Me From Basic Level To Top Level ( I Need Complete Details ) ( But It Must Be Easy To Understand )

---------------------------------------------------------------------------------------------

Thanks In Advance ;)

 

[jeppetrost]

Angles (solid or not) are a measure of how far around a cirlce you've gone. Given a circle, an angle (in radians) tells you the how far around the circle you've gone in terms of its radius. So if you've gone one 'radius' along the circumference, then the angle (seen in the center of the circle) between your starting point and your end point is 1 radian.

The same principle goes for solid angles. Here we are looking at a sphere, and instead of a distance along a circle, you have an area on the sphere. The solid angle tells you how much this area is in terms of the radius of the sphere squared.

This should also hint as to why we measure angles from 0 to 2pi (the circumference of a circle is 2*pi*r) and solid angles from 0 to 4pi (the area of a sphere is 4*pi*r^2).

By the way, what do you mean with "supplementary quantities" ?

 

[Kehsibashok]

Angles (solid or not) are a measure of how far around a cirlce you've gone. Given a circle, an angle (in radians) tells you the how far around the circle you've gone in terms of its radius. So if you've gone one 'radius' along the circumference, then the angle (seen in the center of the circle) between your starting point and your end point is 1 radian.

The same principle goes for solid angles. Here we are looking at a sphere, and instead of a distance along a circle, you have an area on the sphere. The solid angle tells you how much this area is in terms of the radius of the sphere squared.

This should also hint as to why we measure angles from 0 to 2pi (the circumference of a circle is 2*pi*r) and solid angles from 0 to 4pi (the area of a sphere is 4*pi*r^2).

By the way, what do you mean with "supplementary quantities" ?

plane and solid angles are collectively called as supplementary quantities.it's a bit confusing . it is better if there is any animated video. :)