How to measure angular velocity and what is the unit of angular veloci

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Discussion Overview

The discussion revolves around measuring angular velocity and understanding its units, particularly in the context of an object being spun in circular motion and subsequently released. Participants explore concepts related to velocity, acceleration, and the implications of relativistic speeds.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants discuss the velocity of an object in circular motion and its transition to linear motion upon release, questioning how to express this velocity.
  • There is a mention of uniform circular motion and the distinction between speed and velocity, with some asserting that the speed remains constant while the velocity vector changes direction.
  • One participant raises a hypothetical scenario about spinning an object at 0.9c and questions the effects on speed when pulling the object inward, invoking conservation of angular momentum.
  • Another participant points out that increasing mass is an outdated concept and suggests that modern physics reclassifies this in terms of relative kinetic energy.
  • Concerns are raised about separating relativistic effects from angular motion and the necessity of considering the observer's frame of reference.
  • There is a discussion about the need for a way to express angular velocity in relation to circular motion, with suggestions of using units like 0.9crad/sec².
  • It is noted that angular velocity cannot be calculated without knowing the radius of the circle.
  • Participants agree that the unit of angular velocity is radians per second.

Areas of Agreement / Disagreement

Participants express differing views on the implications of spinning an object at relativistic speeds and the nature of angular velocity. While there is some agreement on the unit of angular velocity, the discussion remains unresolved regarding the relationship between circular motion and linear velocity upon release.

Contextual Notes

Limitations include the dependence on the radius of the circular path for calculating angular velocity and the unresolved nature of relativistic effects on angular momentum and velocity.

Sreenath Skr
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Let's say i spin an object around me with a greate velocity.
At some point, i leave that object and it moves in a straight direction with a velocity of 0.9c.
If so what was its velocity while it was revolving around me? How do i experes it?
 
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Sreenath Skr said:
Let's say i spin an object around me with a greate velocity.
At some point, i leave that object and it moves in a straight direction with a velocity of 0.9c.
If so what was its velocity while it was revolving around me?

If you have an object attached to a string and spin it around above your head at a steady speed, that's a model of uniform circular motion:
http://en.wikipedia.org/wiki/Uniform_circular_motion#Uniform

Speed is a rate of motion. In physics, velocity also includes direction. The speed is consistent but the velocity constantly changes because the velocity vector is always tangent to the circumference of the circle. If the object travels at .9c when released, that is also the speed it was traveling at in circular motion.

How do I experes it?

I'm not sure what part of the process you're asking about. Is it the circular motion, the speed, velocity vector...? Perhaps the link to the wiki will help explain more.

EDIT: I just noticed the title of your post indicates angular velocity. Units for that would radians/sec. The wiki link includes formulas and units for everything related to angular velocity.
 
Last edited:
I have a question about the reverse thought in this original question. If it was possible to spin this object around at 0.9c what would happen to the speed of the "object" if you were to pull it in toward you? Wouldn't conservation of angular momentum (say in a vacuum) cause the "object" to increase its speed until it was traveling at greater than c or would it's increasing mass simply cause the center (you, in this thought experiment) to slow its rotation so that the "object" never could increase to this greater than c velocity?
 
MikusF318 said:
I have a question about the reverse thought in this original question. If it was possible to spin this object around at 0.9c what would happen to the speed of the "object" if you were to pull it in toward you? Wouldn't conservation of angular momentum (say in a vacuum) cause the "object" to increase its speed until it was traveling at greater than c...

Although the OP specified .9c as the rate of motion, the explanations have been O.K. so far using classical modeling. Your new question requires moving into relativistic modeling.

...or would it's increasing mass simply cause the center (you, in this thought experiment) to slow its rotation so that the "object" never could increase to this greater than c velocity?

Increasing mass is an historical explanation that has fallen by the wayside in modern physics. Terminology today usually means "inertial mass" - the mass when measured in a "rest frame". "Additional mass" due to relative velocity has been reclassified/translated to relative kinetic energy. This makes great sense because it agrees with how different observers measure and confirm consistent metrics that consistently adhere to the physical laws of 'systems'. (Standing by for corrections from knowledgeable members if my terminology is lacking... :smile:)

To move on with your question, I think it could be O.K. to separate the relativistic velocity aspects from the angular motion. We also need to introduce an observer, and that would be you. Whether you attempt to add velocity to a mass in a circular motion or a straight path, mathematical transformations of relativity will introduce time dilation, length contraction, and other aspects that are dependent on the frame of the observer. Without drilling deeper into relativistic aspects, any perceived addition to the relative rate of motion of the object on the 'string' will adhere to relativistic formulas for adding velocities. This will always keep the relative speed less than c.
 
TumblingDice said:
If the object travels at .9c when released, that is also the speed it was traveling at in circular motion.

But i can't say it was traveling at 0.9c in cirular motion. Circular motion is accelerative so i mean there has to be a way to tell it

Like this 0.9crad/sec²?
 
Sreenath Skr said:
But i can't say it was traveling at 0.9c in cirular motion. Circular motion is accelerative so i mean there has to be a way to tell it

Like this 0.9crad/sec²?

The acceleration in circular motion is perpendicular to the circumference of the circle. The velocity vector remains tangent to the circumference. Take a look at the graphic illustrations in the wiki link. You'll see v(t) is always tangent to the circumference and is the direction the object will continue along when released.

The angular velocity cannot be calculated without knowing the radius of the circle.
 
...and what is the unit of angular veloci

Radians per second.
 

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