# Determining unit vector of acceleration and velocity in circular motio

1. Jan 13, 2014

### negation

As a particle orbits around a circle, the unit vector of the velocity and acceleration component is constantly changing, so, how do I determine the unit vector?

2. Jan 13, 2014

### Simon Bridge

The unit vector for, say, velocity, is the velocity vector divided by the vector-magnitude - same as for any motion.
What is the problem? Can you provide an example where a difficulty arises?

$$\vec v = v\hat v: \hat v = \frac{\vec v}{v}$$

eg. Circular motion about origin at constant speed v and radius R, in Cartesian coordinates:

$\vec r (t) = \hat\imath R\sin\omega t + \hat\jmath R\cos\omega t : v=R\omega$

The unit vector for position would be:

$\hat r = \hat\imath \sin\omega t + \hat\jmath \cos\omega t$

Last edited: Jan 13, 2014
3. Jan 13, 2014

### negation

Just as I suspected. I wanted to confirm my understanding.
Thanks for the input.

4. Jan 13, 2014

### Simon Bridge

Gah - I think I got suckered: well done!