## How do you find velocity in spherical coordinates?

- Vx, Vy, and Vz be the x,y, and z components of the velocity V in Cartesian co-ordinates i.e.
- V= iVx + jVy + kVz.
- Then the r, th, ph components of V in spherical coordinates are given by.
- Vr = |V| = sqrt(Vx^2+Vy^2+Vz^2) . . . . . (
- Vth = Vz . . . . . . . . . ( 2) and.
- Vph = V cos(ph_v) = Vcos[atan2(Vx,Vy)] . . . . . (

**How do you find velocity and acceleration from spherical coordinates?**

Three-Dimensional Spherical Coordinates ∴ˆr=(cosθ˙θcosϕ−sinθsinϕ˙ϕ)ˆx+(cosθ˙θsinϕ+sinθcosϕ˙ϕ)ˆy−sinθ˙θˆz. The radial, meridional and azimuthal components of velocity are therefore ˙r, r˙θ and rsinθ˙ϕ respectively. The acceleration is found by differentiation of Equation 3.4. 15.

**Why do we prefer a spherical coordinate system?**

Spherical coordinates determine the position of a point in three-dimensional space based on the distance ρ from the origin and two angles θ and ϕ. If one is familiar with polar coordinates, then the angle θ isn’t too difficult to understand as it is essentially the same as the angle θ from polar coordinates.

### How do you convert coordinates to vectors?

Just as in two-dimensions, we assign coordinates of a vector a by translating its tail to the origin and finding the coordinates of the point at its head. In this way, we can write the vector as a=(a1,a2,a3).

**What are spherical polar coordinates derive an expression for velocity in spherical polar coordinates?**

In spherical polar coordinates, h r = 1 , and , which has the same meaning as in cylindrical coordinates, has the value h φ = ρ ; if we express in the spherical coordinates we get h φ = r sin θ . Finally, we note that h θ = r . (6.21) (6.22)

**What is curl in spherical coordinates?**

Curl of a vector field is a measure of circulating nature or whirling nature of an vector field at the given point. If the field lines are circulating around the given point leading to net circulation, signifies the Curl. The net circulation may be positive or negative. The uniform vector field posses zero curl.