Circular motion angular velocity

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Homework Help Overview

The discussion revolves around the concept of angular velocity in the context of circular motion. The original poster presents a general question about determining the angular velocity of a particle moving in a plane relative to a reference point, given the particle's velocity vector and position vector.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster describes a technique involving the perpendicular component of velocity and its relation to the distance from the reference point. They express uncertainty about the validity of this method and its connection to the formula v=rw from circular motion.

Discussion Status

Some participants provide affirmations and clarifications regarding the method, suggesting that the projection of velocity onto a circular path is relevant for calculating angular velocity. There is an ongoing exploration of the relationship between linear velocity and angular displacement.

Contextual Notes

The original poster seeks help in understanding the method and its derivation, indicating a potential gap in their grasp of the underlying concepts of angular motion.

Abhishekdas
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Circular motion...angular velocity...

Homework Statement


This is a general question i have...Lets say a particle is moving in a plane (in any arbitrary way may or maynot be following any equation)...Now we are told to find the angular velocity of the particle with respect to a reference point at some instant...lets say you have the velocity vector of the particle and the position vector of the particle with respect to the reference point(or simply the distance between them).

Homework Equations





The Attempt at a Solution


A technique i came across(which i guess is common) is to take the component of the velocity which is perpendicular to the line joining the point and the particle and then dividing it by the distance between them.

Now does this method comes from analogy with circular motion where v=rw? I am not totally convinced by this method and i don't understand this properly...So please help...
 
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Hi Abhishekdas! :wink:
Abhishekdas said:
A technique i came across(which i guess is common) is to take the component of the velocity which is perpendicular to the line joining the point and the particle and then dividing it by the distance between them.

Now does this method comes from analogy with circular motion where v=rw? I am not totally convinced by this method and i don't understand this properly...So please help...

Yes, that's fine …

angular velocity = angle per time,

and to find the angle you're only interested in the projection of the velocity on a circle, ie the component of the velocity perpendicular to the line joining the point and the particle …

so you find that projection (an arc of a circle), then divide by the radius to get the angle :smile:
 


Hey thanks tiny-tim... i think i am kind of getting it...
Is it like the actual velocity is the hypotenuse of a right angled triangle and the base ie the projection is approximated as the arc and then it iss arc = r*d(theta)...
Am i thinking correctly?
 
Yes that's right …

component and projection are the same thing. :smile:
 


ya...Thanks...got it...
 

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