According to the theory of relativity
time slows down for any kind of motion including spinning motion.
Any rotational motion (RPM) can be converted into it's linear velocity (km/sec) equivalent
if the circumference of the spinning sphere is known.
Thus with each full rotation a linear distance equivalent to the sphere's circumference is traversed.
For example, where the equatorial circumference of a sphere is 6,000 km,
(in one complete revolution it traverses a distance of 6000 km)
If it takes one minute to complete a single revolution, 1 rpm = 6,000 km /60 sec = 100 km /sec
Question:
How fast would this sphere have to spin to attain a linear velocity equal to the speed of light (300,000 km/sec)?
Answer:
A sphere of this circumference (6000 km) ,would need to rotate at
300,000/100 = 3000 rpm = 50 hertz (rps)
300,000/100 = 3000 rpm = 50 hertz (rps)
..and the smaller the circumference of the sphere ,the faster it would need to spin/rotate.
Thus a sphere rotating at 100 Hz would attaain light velocity if it were 3000 km in circumference
And a sphere rotating at 1000 Hz would only need to be 300 km in circumference.
Assuming that no object can spin faster than light speed, ..if the maximum rotational speed of an object is limited by the object's size/circumference ,it should be possible to formulate a mathematical relationship betwween an objects spin velocity (rpm) and it's circumference.
That is, the maximum rotational speed that a sphere can attain (assuming this maximum to be equal to light speed)
depends upon the circumference of the sphere!
How would this translate into the quantum realm of spinning subatomic particles?
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The following is from Wikipedia:
Current theories of neutron star structure and evolution predict that pulsars would break apart if they spun at a rate of ~1500 rotations per second or more,[7][8] and that at a rate of above about 1000 rotations per second they would lose energy by gravitational radiation faster than the accretion process would speed them up.[9]
However, in early 2007 data from the Rossi X-ray Timing Explorer and INTEGRAL spacecraft discovered a neutron star XTE J1739-285 rotating at 1122 Hz.[10] The result is not statistically significant, with a significance level of only 3 sigma. Therefore, while it is an interesting candidate for further observations, current results are inconclusive. Still, it is believed that gravitational radiation plays a role in slowing the rate of rotation. Furthermore, one X-ray pulsar that spins at 599 revolutions per second, IGR J00291 plus 5934|IGR J00291+5934, is a prime candidate for helping detect such waves in the future (most such X-ray pulsars only spin at around 300 rotations per second).
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According to Newton's First law:
The velocity of a body remains constant unless the body is acted upon by an external force
This means that to increase the rate of motion of an object requires an input of energy.
This energy input is stored as the sum of the objects mass (potential energy) and it's kinetic energy (energy of rotational and translational motion)
This is why the mass/energy (E=mc^2) of an object increases as it's rate of motion increases (upto the speed of light)
Light velocity ("C") is a fixed ratio between space and time.
This fixed ratio (d/t) is 300,000 km/second.
In order to maintain this ratio,.. as space expands, clocks must run faster.
That is the flow of time must speed up.
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The conservation of angular momentum is a corollary of Newton's First Law
angular momentum is sometimes described as the rotational analog of linear momentum.
the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The very high rotational rates of neutron stars can also be explained in terms of angular momentum conservation
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It seems that all objects possessing mass from subatomic patricles to the universe itself ,possess spin or rotational velocity
As gravity compresses matter/energy into a smaller volume (denser core) it also increases the rate of spin of the object.
When an object such as a flywheel or a subatomic particle such as a proton spins, it serves as a reservoir of (kinetic) energy.The higher the velocity or rate of spin,the more energy it contains.
Much of the energy contained/confined within nucleons is in this form.
When referring to a particle being at rest (meaning no linear velocity) this does not exclude it's rotational velocity/motion.
Light velocity ("C") is a fixed ratio between space and time.
This fixed ratio (d/t) is 300,000 km/second.
In order to maintain this ratio,.. as space expands, clocks must run faster.
That is the flow of time must speed up.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The conservation of angular momentum is a corollary of Newton's First Law
angular momentum is sometimes described as the rotational analog of linear momentum.
the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The very high rotational rates of neutron stars can also be explained in terms of angular momentum conservation
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It seems that all objects possessing mass from subatomic patricles to the universe itself ,possess spin or rotational velocity
As gravity compresses matter/energy into a smaller volume (denser core) it also increases the rate of spin of the object.
When an object such as a flywheel or a subatomic particle such as a proton spins, it serves as a reservoir of (kinetic) energy.The higher the velocity or rate of spin,the more energy it contains.
Much of the energy contained/confined within nucleons is in this form.
When referring to a particle being at rest (meaning no linear velocity) this does not exclude it's rotational velocity/motion.
What is the mechanism whereby energy acquires mass and is transformed into matter?
ReplyDeleteWhat is the rotational velocity of a neutron?
ReplyDeleteDoes a photon have spin(rotational motion)?
We think of light as always being in motion--moving with a linear velocity of 300,000 km/s.
But if we visualize it as a spherical particle with some finite volume and circumference,
all it's linear velocity could be mathematically converted into an equivalent rotational velocity. It's energy content would be conserved and light would then be in a state of rest (zero linear velocity) with respect to linear motion.
This may be the mechanism whereby the kinetic energy of a photon is converted into the stored energy of a particle possessing mass.
So the corollary of this would be the conversion of mass into forward motion? ...or the conversion of potential into kinetic energy.
DeleteWhat would a photon look like if it stopped (i.e. if it had zero velocity)?
DeleteWhat is the "mass-equivalent of a photon?
since,
Deletee=mc2
therefore,
m=e/c2
Would a "stopped" photon still be a photon?
Photons also possess spin and so exhibit a similar SHE. But the effect is extremely weak thanks to the fact that photons have a very small momentum compared with electrons. "The photonic SHE is very weak because the spin angular momentum of photons and spin–orbit interactions are basically negligible," says Xiang Zhang of the Lawrence Berkeley National Laboratory's Materials Sciences Division, who is one of the authors of the new research, published in Science. He points out that while other experiments have tried to detect the photonic SHE using techniques such as weak measurements, the effect observed has always been very small.
DeleteScience 22 March 2013:
Vol. 339 no. 6126 pp. 1405-1407
DOI: 10.1126/science.1231758
•Report
Photonic Spin Hall Effect at Metasurfaces
Xiaobo Yin1,2,
Ziliang Ye1,
Junsuk Rho1,
Yuan Wang1,
Xiang Zhang1,2,*
Remember it is commonly held that photons exhibit dual charactertistics of being a particle or a wave (or both).
ReplyDeleteIf visualized as a spherical particle, such a particle would presumably have some finite dimensions.(i.e. a diameter and a circumference)
If we represent a photon as a sphere/particle with a diameter equal to its wavelenght( say 1000 nm)...what would its spin velocity be if all its linear velocity(300,000 km/s) were completely converted to spin velocity?
First calculate the circumference of the sphere:
The circumference of a circle can be found by multiplying pi
( π = 3.14 ) by the diameter of the circle.
If a circle has a diameter of 4, its circumference is 3.14 x 4=12.56
So then a photon "particle" with a diameter of 1000 nm would have a circumference of 3.14 x 10^3 nm.
So now we can convert linear motion (meters/second)into stationary motion or rotational motion:
The linear speed of light is 300,000 km/s = 300,000,000 m/s
= 3 x 10^8 m/s
At 3 x 10^8 m/s how much time (i.e. how many seconds) would it take to cover a distance of 3.14 x 10^3 nm (wch is one revolution)? (3140 nanometers = 3.14 × 10^-6 meters)
ReplyDeleteLooks like one revolution would take 3.3 x 10^-7 seconds....wch is 1x10^12 rps (revolutions per second)
Assuming that nothing can move faster than the speed at wch light moves. ..
Deletethis means there is a calculatable upper "spin limit" for any particle.
The smaller the particle, the higher its "spin limit".
If an object/particle is spinning as fast as it can(that is, at its "spin limit"),does this mean it is not allowed to also have linear motion/velocity?
DeleteIT is known that the faster an object spins, the more energy it possesses...and as an object approaches light speed
ReplyDeleteits mass(energy content) also increases.
So how is the sum of the kinetic energy(linear or translatioal velocity)and the stationary motion(spin velocity) of an object related to its total mass?
Is the total energy content of a mass equal to the sum of these
two velocities?
What are the highest measured rotational velocities of neutron stars? 1/4 C, 3/4 C ?
ReplyDeletePulsars are neutron stars that rotate at very high speeds and appear to emit radio pulses at extremely regular intervals. The pulses are actually all we see of a radio beam that is focused by the star's magnetic field and swept around like a lighthouse beacon. Using a radio telescope, astronomers can measure the arrival times of successive pulses to a precision of 100 ns over a measurement time of about an hour.
The frequency of a pulsar drops slowly with time as rotational energy is radiated away,
Rotational velocity of a Black Hole:
ReplyDeleteRisaliti and colleagues concluded that the spinning black hole did affect the X-rays emitted from the accretion disc. The study confirms that the SMBH is spinning at a rate close to the limit defined by the general theory of relativity.
While the rotational properties of a spinning gravitational singularity are difficult to describe in a simple way, Risaliti explains that the rotational energy of the SMBH at the heart of NGC1365 is about the same as the energy that is given off by a billion stars burning for a billion years.
http://www.nature.com/nature/journal/v494/n7438/full/nature11938.html
The spin rate of Black Hole has been measured!
Deletehttp://en-maktoob.news.yahoo.com/black-hole-spinning-speed-light-052416024.html
http://in.news.yahoo.com/spin-rate-supermassive-black-hole-estimated-first-time-055247335.html
Can Black Holes spin faster than the speed of light?
Deletehow fast do Black Holes spin?
“unambiguous measurement of the spin rate” of a supermassive black hole: (670 million mph=1.08 billion kph).
light speed is 1080 million (1.08×10^9)kph = 671 million (6.71×10^8)mph
http://www.nature.com/news/spin-rate-of-black-holes-pinned-down-1.13512
http://news.yahoo.com/black-holes-galaxies-rotate-fast-study-finds-183938242.htm
"the limit defined by the general theory of relativity."
ReplyDeletethis limit is the speed of light.
Neutron stars are the collapsed cores of stars. They have extreme mass densities,
ReplyDeleteextreme rotational velocities, and powerful magnetic fields powering high energy blasts of radiation.
A teaspoon of neutrons weighs ten million tons on earth (this is equivalent to collapsing the sun into a sphere just
20 km in diameter)
They can rotate 700 times per second (rps) or 42,000 rpm
Most exhibit highly stable rotational velocities,but some exhibit sudden changes in their rotational rate--either speeding up or slowing down.
For the rotational velocity to speed up would require an input of energy.
Perhaps this energy absorption occurs through tbe capture of a neighboring mass
by the neutron star's powerful gravitational field. (a corollery of this is that Black Holes absorb mass/energy)
An alternative hypothesis is that neutron stars conzist of an outer crust and an interl
internal fluid plasma and the inner and outer components spin at different rates.
The inner fluid can on occasion couple to the outer layer thereby altering the observable velocity of rotation.
Alternatively a slowing down of a neutron star's rate of spin might be accounted for by a massive outburst of radiation energy resulting in a corresponding reduction in the star's mass. Since the Black Holes at the center of galaxies are continuosly sucking up
matter/energy by virtue of tbeir powerful gravitational field , the rotational velocity of Black Holes would be predicted to speed up with time. Although the time scale of this change may be so long that the velocity change may not be detectible/observable, it should nevertheless be calculatable mathematically.
How much of a galaxy's total mass is contained within the event horizon of it's Black Hole?