Circular motion angular velocity

In summary, the technique to find the angular velocity is to take the perpendicular component of the velocity and divide by the distance between the point and the particle.
  • #1
Abhishekdas
208
0
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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  • #2
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:
 
  • #3


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?
 
  • #4
Yes that's right …

component and projection are the same thing. :smile:
 
  • #5


ya...Thanks...got it...
 

FAQ: Circular motion angular velocity

What is circular motion angular velocity?

Circular motion angular velocity is the rate at which an object rotates or moves around a central axis in a circular path. It is measured in radians per second or degrees per second.

How is circular motion angular velocity calculated?

Circular motion angular velocity can be calculated by dividing the angular displacement (change in angle) by the time it takes to complete that displacement. It can also be calculated by dividing the linear velocity (speed of an object in a circular path) by the radius of the circle.

What is the difference between angular velocity and linear velocity?

Angular velocity is the rate of change of angular displacement, while linear velocity is the rate of change of linear displacement. In other words, angular velocity measures how fast an object is rotating, while linear velocity measures how fast an object is moving in a straight line.

How does angular velocity relate to centripetal acceleration?

Angular velocity and centripetal acceleration are directly proportional. This means that as angular velocity increases, so does centripetal acceleration. This is because an increase in angular velocity results in a greater change in velocity, which requires a greater centripetal force to keep the object in circular motion.

What are some real-life examples of circular motion angular velocity?

Some real-life examples of circular motion angular velocity include the rotation of a Ferris wheel, the motion of a spinning top or gyroscope, the rotation of the Earth on its axis, and the orbit of planets around the sun.

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