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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?
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 ##
A unit vector is a vector with a magnitude of 1 and is used to represent a direction in space.
The unit vector of acceleration in circular motion is determined by dividing the acceleration vector by its magnitude, resulting in a vector with a magnitude of 1 pointing in the same direction as the original acceleration vector.
The unit vector of velocity in circular motion is a vector with a magnitude of 1 pointing in the direction of the tangent to the circular path at a specific point.
The unit vector of velocity in circular motion is calculated by dividing the velocity vector by its magnitude, resulting in a vector with a magnitude of 1 pointing in the same direction as the original velocity vector.
Determining the unit vectors of acceleration and velocity in circular motion allows us to understand the direction of these vectors and their relationship to the circular path. This information is crucial in analyzing circular motion and can help us make predictions and calculations about the motion.