- #1
zeromodz
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If so, wouldn't gamma would be like?
(1 - w^2 / c^2)^-1/2
or
(1 - v^2 / r^2c^2)^-1/2
(1 - w^2 / c^2)^-1/2
or
(1 - v^2 / r^2c^2)^-1/2
torquil said:First of all, you're better of doing a detailed calculation of it than to guess. Your expressions are not dimensionally correct.
Your first expression must be incorrect because c has units length/time, and w presumable has units 1/time since I'm guessing it is an angular velocity. So w^2/c^2 is not dimensionless as it should be since it is subtracted from the dimensionless quantity 1.
The same goes for the second expression, v^2/(r^2*c^2) is not dimensionless if v is an ordinary velocity of dimension length/time, and r is a length.
Consider a particle moving in a circle at radius r with a tangential velocity v. The gamma factor you'd get in your expressions would still be
gamma = 1/sqrt(1-v^2/c^2)
But if you want you may express it in terms of an angular velocity w by defining w := v/r and then you get
gamma = 1/sqrt(1- w^2*r^2/c^2)
Or you could use some factors of Pi if you like in your definition of the angular velocity. They would then appear in gamma aswell.
zeromodz said:So that means
gamma = 1/sqrt(1- w^2*r^2/c^2)
is the correct formula to use. Also, nobody answered that there really is relativistic angular velocity. Does something way more if it spins really really fast?
Relativistic angular velocity is a measure of how fast an object is rotating or spinning relative to an observer's frame of reference, taking into account the effects of special relativity.
Relativistic angular velocity takes into account the effects of special relativity, such as time dilation and length contraction, while classical angular velocity does not. This means that relativistic angular velocity can be different depending on the observer's reference frame, while classical angular velocity is always the same regardless of the observer.
Yes, an object can have a relativistic angular velocity if it is moving at a significant fraction of the speed of light. In this case, the object's rotation will appear different to observers in different reference frames due to the effects of relativity.
Relativistic angular velocity is calculated using the formula ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the distance from the axis of rotation. However, this formula only applies in cases where the object's speed is much less than the speed of light. For higher speeds, more complex formulas that take into account the effects of relativity must be used.
One example of relativistic angular velocity is the rotation of a neutron star. Due to its high speed and intense gravity, a neutron star's rotation appears different to observers on Earth compared to observers in a different reference frame. Another example is the rotation of particles in a particle accelerator, which can reach speeds close to the speed of light and therefore exhibit relativistic effects.