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2022-09-14: Could the Higgs Boson Lead Us to Dark Matter?
- 03:35: The second family of experiments, indirect detection, can be represented by rotating our Feynman diagram.
- 04:41: OK, let’s try rotating our Feynman diagram one more time.
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2022-06-01: What If Physics IS NOT Describing Reality?
- 05:53: ... question “are you pointing left or right?” We can do this by rotating the Stern Gerlach apparatus 90 degrees. You started out with ...
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2021-11-10: What If Our Understanding of Gravity Is Wrong?
- 00:24: ... the early 60s, Vera Rubin proved that the spiral galaxies are rotating so fast that they should fling themselves apart - assuming they ...
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2021-09-21: How Electron Spin Makes Matter Possible
- 00:26: ... all about that recently - how electrons have spin but aren’t really rotating. And about how you need to turn an electron around twice - 720 degrees - ...
- 03:19: ... that previous episode we saw this amazing animation of an object rotating while being fixed by bands to it's surrounding environment. Crazily the ...
- 03:46: ... degrees so you have a double twist. Now I’m going to untwist it without rotating either end of the belt. Watch. Now at this point I am letting go of the ...
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2021-08-10: How to Communicate Across the Quantum Multiverse
- 14:53: ... comment by awuma to help answer this. Awuma tells us that such rapidly rotating white dwarfs are found in post-common envelope close binary systems - ...
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2021-08-03: How An Extreme New Star Could Change All Cosmology
- 00:47: ... was seen in its rapid but periodic flickering - suggesting that it was rotating several times every ...
- 02:13: ... to a few days to rotate. But it’s hard to see how any star could be rotating fast enough to produce a white dwarf that spins every 7 ...
- 08:48: ... - but that’s not so strange in itself. The strange part is that it’s rotating extremely quickly and has a crazy strong magnetic field. We just don’t ...
- 02:13: ... to a few days to rotate. But it’s hard to see how any star could be rotating fast enough to produce a white dwarf that spins every 7 ...
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2021-07-07: Electrons DO NOT Spin
- 00:47: ... and switch on a vertical magnetic field. The cylinder immediately starts rotating with a constant speed. At first glance this appears to violate ...
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2021-04-07: Why the Muon g-2 Results Are So Exciting!
- 03:43: For a rotating charge, that depends on the objects rate of rotation, or angular momentum, it's charge and it's mass.
- 03:50: Here's the equation for the classical dipole moment for a nonquantum rotating charge.
- 04:15: So the electron responds to a magnetic field twice as strongly compared to what you'd expect for an equivalent classical rotating charge.
- 03:43: For a rotating charge, that depends on the objects rate of rotation, or angular momentum, it's charge and it's mass.
- 03:50: Here's the equation for the classical dipole moment for a nonquantum rotating charge.
- 04:15: So the electron responds to a magnetic field twice as strongly compared to what you'd expect for an equivalent classical rotating charge.
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2021-02-17: Gravitational Wave Background Discovered?
- 00:00: ... pulsar sounds like that's the sound of a trillion trillion trillion tons rotating 1.4 times per second and this is the crab pulsar with its 30 rotations ...
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2021-02-10: How Does Gravity Warp the Flow of Time?
- 06:11: If we set it rotating at the right speed then centripetal acceleration leads to some nice artificial gravity.
- 07:01: And it turns out that the stationary clock did tick more - time slowed for the rotating case.
- 07:52: Here’s the spacetime diagram for our rotating lab.
- 10:17: ... orbital motion in a gravitational field is very different from our rotating space station- then both gravitational time dilation and kinematic time ...
- 07:01: And it turns out that the stationary clock did tick more - time slowed for the rotating case.
- 07:52: Here’s the spacetime diagram for our rotating lab.
- 10:17: ... orbital motion in a gravitational field is very different from our rotating space station- then both gravitational time dilation and kinematic time ...
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2020-12-22: Navigating with Quantum Entanglement
- 04:56: Magnetic fields exert a force on a moving or rotating charged particle.
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2020-10-27: How The Penrose Singularity Theorem Predicts The End of Space Time
- 03:18: ... to the mid 1960s. Roy Kerr has just figured out how to describe a rotating black hole in Einstein’s theory. In it, the ...
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2020-08-24: Can Future Colliders Break the Standard Model?
- 14:49: Think of the case of the rotating black hole - the singularity is a ring, and relatively few geodesics - free-falling paths - hit the singularity.
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2020-08-17: How Stars Destroy Each Other
- 06:03: ... flares, resulting from denser clumps of material hitting the rapidly rotating surface of the neutron ...
- 13:42: ... into an ovoid and then finally a sphere, or flattened sphere for a rotating black ...
- 06:03: ... flares, resulting from denser clumps of material hitting the rapidly rotating surface of the neutron ...
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2020-06-30: Dissolving an Event Horizon
- 02:51: In recent episodes we also explored the rotating, or Kerr black hole.
- 04:33: And just as with the rotating black hole, at some point the inner and outer horizons become one and vanish and you’re left with a naked singularity.
- 06:06: This can’t happen with rotating black holes because they leak away their angular momentum as well as their mass.
- 07:11: Rotating black holes gain their angular momentum from things they swallow.
- 07:49: The faster a black hole is rotating, the more angular momentum that gas has to lose in order to fall in.
- 07:55: ... because space gets dragged around the rotating black hole, giving the gas a sort of boost so it can still orbit even ...
- 08:06: ... the case of an extremal Kerr black hole - one that’s rotating nearly fast enough to lose its event horizon - the gas near the event ...
- 04:33: And just as with the rotating black hole, at some point the inner and outer horizons become one and vanish and you’re left with a naked singularity.
- 06:06: This can’t happen with rotating black holes because they leak away their angular momentum as well as their mass.
- 07:11: Rotating black holes gain their angular momentum from things they swallow.
- 07:55: ... because space gets dragged around the rotating black hole, giving the gas a sort of boost so it can still orbit even with ...
- 04:33: And just as with the rotating black hole, at some point the inner and outer horizons become one and vanish and you’re left with a naked singularity.
- 07:55: ... because space gets dragged around the rotating black hole, giving the gas a sort of boost so it can still orbit even with very ...
- 06:06: This can’t happen with rotating black holes because they leak away their angular momentum as well as their mass.
- 07:11: Rotating black holes gain their angular momentum from things they swallow.
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2020-06-22: Building Black Holes in a Lab
- 07:41: ... for spinning black holes in particular. Now we’ve looked deeply into rotating, or Kerr black holes recently. Very deeply in fact - we’ve traveled ...
- 08:04: ... thing we saw was that rotating black holes can donate some of their rotational energy to particles or ...
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2020-05-27: Does Gravity Require Extra Dimensions?
- 10:28: In some cases, rotating masses produce oscillations in the torsion pendulum.
- 13:29: ... talked about the strange regions that lie beneath the event horizon of a rotating black hole - regions like the Carter time machine and the infinite ...
- 15:33: ... the string of universes through the rotating Kerr black hole requires the assumption that the impossibly unstable ...
- 13:29: ... talked about the strange regions that lie beneath the event horizon of a rotating black hole - regions like the Carter time machine and the infinite string of ...
- 15:33: ... the string of universes through the rotating Kerr black hole requires the assumption that the impossibly unstable inner ...
- 10:28: In some cases, rotating masses produce oscillations in the torsion pendulum.
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2020-05-18: Mapping the Multiverse
- 00:09: ... english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not come to an abrupt halt at the bottom ...
- 00:36: ... we began a little while ago when we explored the region just above a rotating black ...
- 01:16: ... that mass is NOT rotating and does not have any electric charge, the result is a Schwarzschild ...
- 01:33: Now, we’re going to focus on rotating black holes here, but a lot of this also applies to charged black holes, as we’ll see.
- 01:41: A rotating black hole is described mathematically by the Kerr metric.
- 01:53: We sometimes call a rotating black hole with no electric charge a Kerr black hole.
- 02:40: The event horizon itself is distorted - wider at the equator than the poles, just like the rotating earth.
- 13:50: Just a little wishful thinking, a rotating black hole, and don’t forget to slip your map in your back pocket.
- 00:09: ... english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not come to an abrupt halt at the bottom of the ...
- 00:36: ... we began a little while ago when we explored the region just above a rotating black ...
- 01:33: Now, we’re going to focus on rotating black holes here, but a lot of this also applies to charged black holes, as we’ll see.
- 01:41: A rotating black hole is described mathematically by the Kerr metric.
- 01:53: We sometimes call a rotating black hole with no electric charge a Kerr black hole.
- 13:50: Just a little wishful thinking, a rotating black hole, and don’t forget to slip your map in your back pocket.
- 00:09: ... english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not come to an abrupt halt at the bottom of the ...
- 00:36: ... we began a little while ago when we explored the region just above a rotating black hole. ...
- 01:41: A rotating black hole is described mathematically by the Kerr metric.
- 01:53: We sometimes call a rotating black hole with no electric charge a Kerr black hole.
- 13:50: Just a little wishful thinking, a rotating black hole, and don’t forget to slip your map in your back pocket.
- 01:33: Now, we’re going to focus on rotating black holes here, but a lot of this also applies to charged black holes, as we’ll see.
- 02:40: The event horizon itself is distorted - wider at the equator than the poles, just like the rotating earth.
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2020-05-11: How Luminiferous Aether Led to Relativity
- 10:02: ... mercury so it would maintain a fixed orientation despite the earth rotating beneath ...
- 10:42: ... the aether wind - if it existed. Of course you know what’s coming - on rotating the device the interference pattern didn’t budge. OK, so maybe the ...
- 10:02: ... mercury so it would maintain a fixed orientation despite the earth rotating beneath ...
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2020-04-22: Will Wormholes Allow Fast Interstellar Travel?
- 11:48: ... that may not need exotic matter - and that’s the wormhole through a rotating or charged black hole. Now I’ve promised a more in-depth episode on ...
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2020-03-31: What’s On The Other Side Of A Black Hole?
- 10:58: ... would allow instant travel between distant locations. And in the case of rotating black holes, the traversable wormhole and even the parallel universe are ...
- 11:37: ... Okay today we’re doing comments for the last two episodes which are on rotating black holes and quantum darwinism. Let’s see what you had to ...
- 13:31: ... is as much rotational energy as the black hole contains. for a maximally rotating black hole that's 40% of its total mass - all released as energy. To put ...
- 10:58: ... would allow instant travel between distant locations. And in the case of rotating black holes, the traversable wormhole and even the parallel universe are not ...
- 11:37: ... Okay today we’re doing comments for the last two episodes which are on rotating black holes and quantum darwinism. Let’s see what you had to ...
- 13:31: ... is as much rotational energy as the black hole contains. for a maximally rotating black hole that's 40% of its total mass - all released as energy. To put that ...
- 10:58: ... would allow instant travel between distant locations. And in the case of rotating black holes, the traversable wormhole and even the parallel universe are not so easy ...
- 11:37: ... Okay today we’re doing comments for the last two episodes which are on rotating black holes and quantum darwinism. Let’s see what you had to ...
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2020-03-24: How Black Holes Spin Space Time
- 00:03: ... there’s one thing cooler than a black hole it’s a rotating black hole. Why? Because we can use them as futuristic power generators, ...
- 01:44: ... attract opposite charges. But essentially all real black holes will be rotating. The spin of a black hole comes from the combined angular momentum of ...
- 02:36: ... nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in 1963, yielding the Kerr metric and ...
- 03:18: It can be used to calculate the path of any body moving near or even within a Kerr black hole - or indeed any rotating mass.
- 03:27: ... look at what the Kerr solution can tell us about the spacetime outside a rotating black hole. We’ll save the even weirder details of the Kerr black hole’s ...
- 03:54: ... start by talking about what is actually rotating in a Kerr black hole. It’s tempting to just say that some physical thing ...
- 04:26: ... In fact it’s possible to construct a black hole in general relativity rotating or otherwise - without any mass. Warp spacetime so it looks like the ...
- 05:14: ... flow of space around a rotating black hole is known as frame-dragging. We see it around any rotating ...
- 05:49: ... like crazy, you must spiral either inwards or outwards. But for a rotating black hole, frame dragging gives a you little extra kick, and so stable ...
- 08:37: ... the event horizon in the rotating case is not spherical - it’s squished at the poles, like the rotating ...
- 11:31: ... gigantic star collapses at the end of its life, and if its core was rotating fast enough, that core will produce a Kerr black hole that can suck more ...
- 12:11: ... Rotating black holes are very real and powerful players in the energetics of our ...
- 00:03: ... there’s one thing cooler than a black hole it’s a rotating black hole. Why? Because we can use them as futuristic power generators, ...
- 03:27: ... look at what the Kerr solution can tell us about the spacetime outside a rotating black hole. We’ll save the even weirder details of the Kerr black hole’s ...
- 05:14: ... flow of space around a rotating black hole is known as frame-dragging. We see it around any rotating mass. In ...
- 05:49: ... like crazy, you must spiral either inwards or outwards. But for a rotating black hole, frame dragging gives a you little extra kick, and so stable orbits ...
- 12:11: ... Rotating black holes are very real and powerful players in the energetics of our ...
- 00:03: ... there’s one thing cooler than a black hole it’s a rotating black hole. Why? Because we can use them as futuristic power generators, ...
- 03:27: ... look at what the Kerr solution can tell us about the spacetime outside a rotating black hole. We’ll save the even weirder details of the Kerr black hole’s interior ...
- 05:14: ... flow of space around a rotating black hole is known as frame-dragging. We see it around any rotating mass. In frame ...
- 05:49: ... like crazy, you must spiral either inwards or outwards. But for a rotating black hole, frame dragging gives a you little extra kick, and so stable orbits exist ...
- 12:11: ... Rotating black holes are very real and powerful players in the energetics of our universe - ...
- 02:36: ... nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in 1963, yielding the Kerr metric and describing ...
- 08:37: ... the event horizon in the rotating case is not spherical - it’s squished at the poles, like the rotating Earth. ...
- 11:31: ... gigantic star collapses at the end of its life, and if its core was rotating fast enough, that core will produce a Kerr black hole that can suck more ...
- 03:18: It can be used to calculate the path of any body moving near or even within a Kerr black hole - or indeed any rotating mass.
- 05:14: ... a rotating black hole is known as frame-dragging. We see it around any rotating mass. In frame dragging, any “freefall” trajectory - the path taken by an ...
- 04:26: ... the exterior of a black hole, and that warping will persist. So what is rotating? Spacetime is ...
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2020-03-16: How Do Quantum States Manifest In The Classical World?
- 02:56: ... has an axis that points in some direction, analogous to the axis of a rotating ball. To measure that spin axis you have to choose what angle you want ...
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2020-01-13: How To Capture Black Holes
- 06:15: ... is similar to how planets form. When a massive object is embedded in a rotating disk, it will exert a gravitational tug on the surrounding particles. ...
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2019-10-21: Is Time Travel Impossible?
- 07:13: It’s simple: just build an infinitely long cylinder of extreme density and set it rotating insanely quickly about its main axis.
- 08:20: His involved an entire universe, rotating about a central axis and with matter and dark energy perfectly balancing it against collapse or expansion.
- 08:46: Another one is the interior of a rotating black hole – a so-called Kerr black hole.
- 07:13: It’s simple: just build an infinitely long cylinder of extreme density and set it rotating insanely quickly about its main axis.
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2019-10-15: Loop Quantum Gravity Explained
- 15:49: ... exposing the singularity to the universe - or in the case of a rotating black hole, an infinite density ...
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2019-10-07: Black Hole Harmonics
- 09:05: .69 means this is a rapidly rotating black hole, which is unsurprising seeing as it just absorbed the orbital angular momentum of two black holes.
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2019-09-23: Is Pluto a Planet?
- 15:31: Kazeshi wants to do O'Neill cylinders or rotating habitats in space.
- 15:45: ... a rotating habitat or cylinder in space can produce the effect of gravity for its ...
- 15:31: Kazeshi wants to do O'Neill cylinders or rotating habitats in space.
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2019-09-16: Could We Terraform Mars?
- 14:16: ... and I’m still a proponent of centrifuge cities – mag-lev rotating habitats to simulate Earth gravity. Also shown rather beautifully in ...
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2019-09-03: Is Earth's Magnetic Field Reversing?
- 03:34: And although the interior is rotating, it’s electrically neutral – so there shouldn’t be an overall electrical current.
- 06:10: So if the entire core is rotating with the Earth then the magnetic field will also rotate.
- 07:27: ... fact any rotating body with a fluid conductor can produce such a field – the Earth, but ...
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2019-07-01: Thorium and the Future of Nuclear Energy
- 16:59: ... very far Frame dragging is the dragging of the fabric of space around a rotating massive object in the case of a black hole it's most obvious effect is ...
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2019-05-01: The Real Science of the EHT Black Hole
- 06:47: If the black hole is rotating then you can get photon orbits over a range of distances.
- 09:56: So the plasma vortex should be rotating in the same direction as the black hole.
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2018-09-20: Quantum Gravity and the Hardest Problem in Physics
- 14:03: It's possible to extract energy from a rotating black hole by throwing in objects on near-miss trajectories.
- 14:09: The rotating black hole drags space around with it.
- 14:22: But rotating black holes are slightly squished.
- 14:03: It's possible to extract energy from a rotating black hole by throwing in objects on near-miss trajectories.
- 14:09: The rotating black hole drags space around with it.
- 14:22: But rotating black holes are slightly squished.
- 14:03: It's possible to extract energy from a rotating black hole by throwing in objects on near-miss trajectories.
- 14:09: The rotating black hole drags space around with it.
- 14:22: But rotating black holes are slightly squished.
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2018-08-15: Quantum Theory's Most Incredible Prediction
- 03:41: ... fields seem intuitive if you think of them as tiny balls of rotating electric charge, except electrons aren't balls and they aren't really ...
- 03:57: And it doesn't really make sense to think of an infinitesimal point as rotating.
- 04:49: Thinking of electrons as little bar magnets or as rotating balls of charge is a nice starting point.
- 03:41: ... fields seem intuitive if you think of them as tiny balls of rotating electric charge, except electrons aren't balls and they aren't really ...
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2018-06-20: The Black Hole Information Paradox
- 05:27: ... called Einstein-Cartan theory, it's predicted that the formation of a rotating black hole gives birth to an entire new universe accessible by a ...
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2018-06-13: What Survives Inside A Black Hole?
- 09:09: The frame dragging around a rotating black hole is rather stronger.
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2018-05-09: How Gaia Changed Astronomy Forever
- 09:44: A popular one seems to be, rotating black holes or harvesting Hawking radiation from black holes.
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2018-04-18: Using Stars to See Gravitational Waves
- 06:06: It monitors dozens of the fastest rotating pulsars, millisecond pulsars, spanning many thousands of light years.
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2018-03-28: The Andromeda-Milky Way Collision
- 00:38: ... has a beautiful spiral structure, spanning its gently rotating disk 220,000 light years in diameter, and a central bulge that hides a ...
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2017-12-20: Extinction by Gamma-Ray Burst
- 03:03: It's even more dangerous if the star was rapidly rotating before it exploded.
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2017-11-29: Citizen Science + Zero-Point Challenge Answer
- 05:15: But there's also Einstein at Home, which searches for LIGO gravitational wave data for signals produced by rotating neutron stars.
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2017-09-28: Are the Fundamental Constants Changing?
- 05:22: They have magnetic fields, just like a little bar magnet, or electric currents rotating in a ring even though there is no actual rotation.
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2017-08-16: Extraterrestrial Superstorms
- 02:06: Earth is, of course, rotating on its axis.
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2017-06-21: Anti-Matter and Quantum Relativity
- 02:40: That doesn't mean that they're actually rotating.
- 02:47: For example, an electron's spin causes them to align themselves with magnetic fields, just like a rotating electric charge would.
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2017-01-25: Why Quasars are so Awesome
- 05:07: This may be due to the magnetic field of a rapidly rotating black hole, but the jury is still out.
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2016-11-16: Strange Stars
- 07:40: ... X-ray Observatory to that spot and found a young pulsar, a rapidly rotating neutron star 10,000 light years ...
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2016-11-09: Did Dark Energy Just Disappear?
- 14:03: My point is that there are plausible options, and a giant rotating maglev ring city in a sealed taurus is actually plausible.
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2016-10-19: The First Humans on Mars
- 06:02: This is possible using a centrifuge, a rotating ring that results in the feeling of an outward force, a centrifugal force, with respect to the ring.
- 06:19: ... would still involve a large rotating ring, but with a sloped, slightly curved outer wall so that the ...
- 06:32: ... centrifuge cities levitating on superconducting magnetic rails and rotating once every few ...
- 06:02: This is possible using a centrifuge, a rotating ring that results in the feeling of an outward force, a centrifugal force, with respect to the ring.
- 06:19: ... would still involve a large rotating ring, but with a sloped, slightly curved outer wall so that the centrifugal ...
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2016-03-23: How Cosmic Inflation Flattened the Universe
- 11:40: It emerges in a rotating reference frame as a force-like term that resists inward motion.
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2016-01-13: When Time Breaks Down
- 01:11: ... rotating gears are comprised of atoms vibrating in metal lattices, bound by ...
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2015-12-09: How to Build a Black Hole
- 11:47: Now, that's tricky because the asteroid will certainly be rotating.
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2015-10-22: Have Gravitational Waves Been Discovered?!?
- 02:00: So a rotating sphere or a cylinder doesn't make waves.
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2015-08-19: Do Events Inside Black Holes Happen?
- 02:11: At a certain point, I see him in suspended animation, not rotating, not progressing, just frozen.
- 11:17: ... rotating black holes, charged black holes, black hole evaporation, what goes on ...
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2015-08-12: Challenge: Which Particle Wins This Race?
- 00:36: That sphere is not rotating, and it's not orbiting any other larger bodies.
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2015-05-06: Should the First Mars Mission Be All Women?
- 09:14: Fortstorm asks, wouldn't a rotating stations have trouble turning because its angular momentum vector would have trouble being shifted?
- 09:52: ... asks, in a rotating ship like "Babylon 5," assuming that you had atmospheric pressure at the ...
- 09:14: Fortstorm asks, wouldn't a rotating stations have trouble turning because its angular momentum vector would have trouble being shifted?
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2015-04-29: What's the Most Realistic Artificial Gravity in Sci-Fi?
- 01:20: ... the only semi-realistic way we know of to get artificial gravity, namely rotating your ...
- 01:51: But what do things look like from the perspective inside the rotating room?
- 02:27: It turns out that there's a simple formula for how big the effective surface gravity produced by this rotating structure would be.
- 02:33: It's just the radius of the rotating structure multiplied by the square of its rotational speed in radians per second.
- 03:05: Let's start with the iconic scene of Frank Poole jogging around the rotating command module in "2001: A Space Odyssey." Poole's height is 1.8 meters.
- 03:56: That apparent departure from straight line motion in rotating reference frames is called the Coriolis effect.
- 04:01: An object's Coriolis acceleration will be proportional to its speed, relative to the rotating frame and the rotation rate of the frame itself.
- 04:40: On the rotating ship, standing up would therefore make your head want to curve forward from the Coriolis effect, knocking you over.
- 08:01: They get correct that you already have to be rotating to feel the artificial gravity.
- 03:05: Let's start with the iconic scene of Frank Poole jogging around the rotating command module in "2001: A Space Odyssey." Poole's height is 1.8 meters.
- 04:01: An object's Coriolis acceleration will be proportional to its speed, relative to the rotating frame and the rotation rate of the frame itself.
- 03:56: That apparent departure from straight line motion in rotating reference frames is called the Coriolis effect.
- 01:51: But what do things look like from the perspective inside the rotating room?
- 04:40: On the rotating ship, standing up would therefore make your head want to curve forward from the Coriolis effect, knocking you over.
- 02:27: It turns out that there's a simple formula for how big the effective surface gravity produced by this rotating structure would be.
- 02:33: It's just the radius of the rotating structure multiplied by the square of its rotational speed in radians per second.
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2015-03-25: Cosmic Microwave Background Explained
- 06:29: ... nearly as much torque application or leverage as you do from actually rotating a gyroscope without changing its ...
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2015-03-18: Can A Starfox Barrel Roll Work In Space?
- 01:29: In a true barrel roll, the whole aircraft moves along a helical path, corkscrewing rather than just rotating around its access while moving straight.
- 02:03: That tendency to keep rotating is called an objects' angular momentum, and physicists represent it by a vector or an arrow.
- 02:41: ... on the top and bottom of each wing, one quick burst to start to ship rotating and then another opposing burst to stop ...
- 03:23: By rotating the flywheel quickly, I end up transferring its angular momentum to myself, so I start spinning.
- 06:25: To compensate, the ship would have to do some wonky rotating as the flywheel flips, in order to keep the total angular momentum vector unchanged.
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