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

1. Jul 13, 2014

Sreenath Skr

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?

2. Jul 13, 2014

TumblingDice

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.

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: Jul 13, 2014
3. Jul 13, 2014

MikusF318

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 travelling 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?

4. Jul 13, 2014

TumblingDice

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.

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... )

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.

5. Jul 16, 2014

Sreenath Skr

But i can't say it was travelling 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/secĀ²?

6. Jul 16, 2014

TumblingDice

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.

7. Jul 16, 2014

CWatters

Radians per second.

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