Determining unit vector of acceleration and velocity in circular motio

1. negation

819
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. Simon Bridge

14,852
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
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3. negation

819
Just as I suspected. I wanted to confirm my understanding.
Thanks for the input.

4. Simon Bridge

14,852
Gah - I think I got suckered: well done!