Register to reply

Determining unit vector of acceleration and velocity in circular motio

Share this thread:
negation
#1
Jan13-14, 08:05 PM
P: 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?
Phys.Org News Partner Physics news on Phys.org
New complex oxides could advance memory devices
Nature's designs inspire research into new light-based technologies
UCI team is first to capture motion of single molecule in real time
Simon Bridge
#2
Jan13-14, 08:47 PM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 13,124
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
#3
Jan13-14, 09:34 PM
P: 819
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
#4
Jan13-14, 09:51 PM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 13,124
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.


Register to reply

Related Discussions
Unit Normal Vector in Acceleration Classical Physics 17
Vector procedure for determining the velocity and acceleration of rotating rigid body Classical Physics 5
Determining velocity/acceleration in vector-unit notation Calculus & Beyond Homework 2
Determining the Uncertainty of a Unit Vector using Error Propagation Introductory Physics Homework 1
Circular motion - determining expression for a position vector Introductory Physics Homework 1