- #1

John004

- 37

- 0

## Homework Statement

The angular velocity vector of a rigid object rotating about the z-axis is given by

**ω**= ω

**z-hat.**At any point in the rotating object, the linear velocity vector is given by

**v**=

**ω**X

**r,**where

**r**is the position vector to that point.

a.) Assuming that ω is constant, evaluate

**v**and

**∇**X

**v**in cylindrical coordinates.

b.) Evaluate

**v**in spherical coordinates.

c.) Evaluate the curl of

**v**in spherical coordinates and show that the resulting expression is equivalent to that given for

**∇**X

**v**in part a.

## Homework Equations

The expressions for the curl in cylindrical and spherical coordinates. Since I don't know how to put the determinant here ill just leave them out.

For spherical

x = r sinθ cosΦ

y = r sinθ sinΦ

z = r cos θ

## The Attempt at a Solution

So I worked out part a correctly (I think) which is in the attachment, but I'm stuck on part b.

b.) So for this part I have to convert

**ω**to spherical coordinates. Since

**ω**only lies along the z-axis, that means that Φ and θ are equal to zero, so

**ω =**ω

**r-hat**

and the position vector in spherical polars is

**r**

R =

R =

**r-hat**

so that means that when I cross

**ω**and

**R**I get zero, I don't know what I'm missing.

#### Attachments

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