Determining unit vector of acceleration and velocity in circular motio


by negation
Tags: acceleration, circular, determining, motio, unit, vector, velocity
negation
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#1
Jan13-14, 08:05 PM
P: 705
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?
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Simon Bridge
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#2
Jan13-14, 08:47 PM
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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 ##
negation
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#3
Jan13-14, 09:34 PM
P: 705
Quote Quote by Simon Bridge View Post
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 ##
Just as I suspected. I wanted to confirm my understanding.
Thanks for the input.

Simon Bridge
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#4
Jan13-14, 09:51 PM
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Determining unit vector of acceleration and velocity in circular motio


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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