Cylindrical Coordinate System | Santa Fe College - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

447

Pages:

2
Author:

Jabin F.

Cylindrical Coordinate System: s - radial vector φ - azimuthal vector z - axial vector s dot φ = 0, φ dot z = 0 s cross φ = +z φ cross z = +s z cross s = +φ z dot z = 0 Length Elements: ds = ds s_hat dlp = s dφ φ_hat dlz = dz z_hat dl = ds s_hat + s dφ φ_hat + dz z_hat Surface Element: ds = s dφ dz s_hat Scurved = integral from 0 to L integral from 0 to 2pi s dφ dz Scurved = 2pi L s disc: ds = sdsdφ(z+2) ds|z=z₀+½ = sdsdφ(-z) ds|z=z₀-½ = sdsdφ(-z) ds = dsdφ(z) [φ=0 to 2π] Volume Element: dv = dsdφdz Volume of Cylinder: dv = ∫∫∫ sdsdφdz dv = a²[2π][z₀+½ - z₀-½] / 2 dv = πa²L

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