The discussion revolves around determining the unit vectors of velocity and acceleration in the context of circular motion. Participants explore the mathematical formulation and conceptual understanding of these unit vectors, particularly in relation to motion along a circular path.
Participants generally agree on the method for calculating unit vectors, but there is an underlying uncertainty regarding the initial question about determining these vectors in a dynamic context.
Some limitations include the potential for misunderstanding the application of unit vectors in changing conditions, as well as the dependence on specific coordinate systems and definitions used in the examples.
This discussion may be useful for students or individuals interested in understanding the mathematical treatment of circular motion and the concept of unit vectors in physics.
Simon Bridge said: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 ##