# Rotate about an axis

## Homework Statement

$$A = (1,1,-2)$$
$$C = (0,1,-5)$$
(in cartesian coordinates)
Let A and C be drawn from a common origin and let C rotate about A with an angular velocity of 2 rad/s. Find the velocity of the head of C.

## Homework Equations

$$v = w x r$$

## The Attempt at a Solution

w = 2 rad/s
I know I have to take the cross product of w and C (w x C = v) but I am having problems making w as a vector. Initially I thought I would use cylindrical coords and say that it's moving in the phi direction, unfortunately I don't know if that assumption is correct.
Can anyone give me a pointer on how I should begin to write w as a vector?

## Answers and Replies

If by w you mean $\omega$, the angular velocity, then the direction of omega is always perpendicular on the plane of the speed v. Use the right-hand-rule: If you curl your fingers in the direction of v, then the thumb (stretched out) is the direction of omega.

For example, the direction of omega for the hands of a clock (assuming they move with constant speed instead of in little jumps) would be into the clock.

Kurdt
Staff Emeritus
Science Advisor
Gold Member
Omega points along the axis of rotation. It makes sense if you think about what the cross product does and the relation between omega, r and v.