Supplementary Units Physics Notes

Supplementary Units Physics Notes

Supplementary Units:

Definitions:
1. Radian: One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

Plane angle dθ = \(\frac{d S}{r}\)
If dS = r, then dQ = 1 rad

2. Steradian: One steradian is the solid angle subtended at the center of a sphere, by that surface which is equal in area to the square of the radius of the sphere.

Solid angle (dΩ) = \(\frac{\text { Normal surfacearea }}{(\text { Radius })^{2}}\)
∴ Solid angle (dΩ) = \(\left(\frac{d A}{r^{2}}\right)\) steradian

If dA = r² then dΩ = 1 steradian
In case of complete surface area, the cubic angle subtained by it
Ω = \(\frac{4 \pi r^{2}}{r^{2}}\) = 4π steradian

Physics Notes