Determining unit vector of acceleration and velocity in circular motio

  1. 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. jcsd
  3. Simon Bridge

    Simon Bridge 14,852
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    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
    1 person likes this.
  4. Just as I suspected. I wanted to confirm my understanding.
    Thanks for the input.
     
  5. Simon Bridge

    Simon Bridge 14,852
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    Gah - I think I got suckered: well done!
    In future - if you want to confirm your understanding, just state your understanding and ask.
     
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