Learn about cylindrical and spherical coordinates in this 5-minute video lesson. Master the conversion techniques of these math concepts by taking an optional quiz.

In cylindrical coordinates, taking the cross product of two vectors results in a vector that is perpendicular to both crossed vectors. For example, r ^ × z ^ = − θ ^, and r ^ × θ ^ = z ^.

Step 1 Drive the continuity equation in cylindrical coordinates. General vector form.

Derive the heat diffusion equation for cylindrical coordinates, and spherical coordinates using the control volume method developed in class.

Question: The Navier-Stokes equation in cylindrical coordinates is expressed as the following r-direction Alternatively, it can be expressed as a) Rigorously show the viscous dissipation terms in the r …

3. Derive the equilibrium equations in cylindrical coordinates: ∂r∂σr + r1 ∂θ∂τ rθ + ∂z∂τ rz + rσr−σθ = 0 ∂r∂τ rθ + r1 ∂θ∂σθ + ∂z∂τ θz +2 rτ rθ = 0 ∂r∂τ rz + r1 ∂θ∂τ θz + ∂z∂σz + rτ rz =0 This is accomplished …

Question: 2. [15.7A: Cylindrical Coordinates] Sketch the following solids, surfaces, curves, and points, altogether in one plot, with labels. For each surface, convert the equation to rectangular and to …

A point P has Cartesian coordinates (3,-4,10). What is the spherical r coordinate of this point?

Cylindrical Coordinates In many practical situations, using a Cartesian coordinate system leads to difficult problems. Often, a change of coordinate system makes the problem more manageable. One …

Unit vector conversions Conversion between unit vectors in Cartesian, cylindrical, and spherical coordinate systems in terms of destination coordinates Cartesian Cylindrical Spherical Cartesia ух + …