law of conservation of angular momentum

In 1934 Jean Leray proved that the Navier–Stokes equations always have solutions "in a generalized sense". Whether a solution stays smooth or can break down into a singularity he could not tell, and nobody could for ninety years. In 2000 the Clay Institute made the question one of its seven Millennium Prize problems.

Water in a tank spins at nearly four revolutions per second, and, as if by magic, a column the size of a dinner table emerges. The vortex lives for dozens of rotations, even though everything around it churns and trembles. Where does such stability come from? The secret is that the vortex is not isolated.

A sculptor looks at a block of marble and sees the figure within, waiting to be freed from excess material. Instead of adding clay, he removes everything that is not part of the form. The authors of a new study on magnetic resonance took a similar approach: rather than complicating the tissue model by adding ever more details, they stripped away the superfluous to reveal the essence.

Two ink reservoirs stand on opposite sides of the cell junction. From them, two types of monomers flow onto the membrane, and when they meet, they form viscous droplets of complexes. The droplets barely move, but the free monomers dart around as fast as perfume molecules in a room.

A thrown stone arcs through the air, but a planet around the Sun follows a closed curve. Why an ellipse, and not a circle or a spiral? Kepler's first law provides the answer, but its usual proof requires heavy computation. This work offers a shorter path — through a single simple ratio of velocities.

Inside an MRI magnet, current flows through a closed superconducting loop, like water circling in a bucket after you give it a spin, it just keeps going on its own. To change that current, you heat the loop with a small heater: it stops being superconducting, becomes an ordinary resistor, and then an external source can 'top up' or 'draw off' current.

Imagine a string stretched between two tuning pegs. The slightest touch makes it vibrate, and from the pitch you can guess exactly how it was plucked. Physicists at the University of Arizona have stretched a similar string — not on a musical instrument, but on a silicon membrane just a hundred nanometers thick.

A laser beam is like a swift vortex that briefly captures a passing electron. As the particle moves through the pulse, its spin (the intrinsic rotation, like a tiny top) experiences a weak kick. After leaving the beam, the top no longer points in the same direction; it has turned a little.

A pendulum weighing a few grains of sand swings on a hair-thin glass fiber. Its motions are so faint that the thermal jostling of air molecules seems like a hurricane. Yet such a pendulum is the key to witnessing quantum wonders in the world of large objects.

A disk of gas and dust spins around the young star HV Tau C, nearly edge-on to us. The James Webb Space Telescope examined its spectrum and detected the glow of hot molecular hydrogen (H₂). This revealed a wide, bipolar wind blasting from the inner regions far beyond the disk.

Seventy-two protoplanetary disks, swirling cocoons of cosmic dust and gas, came under the gaze of the MIRI instrument on JWST. Most of them shoot outflows into space: dense conical structures and narrow, high-speed jets. They blast like fountains. This process is not accidental.

Two hundred and eighty-nine days: that's how long one rotation of the white dwarf white dwarf WD 1532+129 takes. This is not just a record: on its surface, near the magnetic poles, scars of iron and other metals appear — silent testimony to planets it has devoured.

89 milliseconds. That's how long a vortex avalanche lasts that abruptly speeds up the rotation of the Vela pulsar — one of the most famous 'glitching' pulsars. Pulsars are rapidly spinning neutron stars born in the collapse of supernovae.

A tiny magnetized sphere floats in a vacuum, held by invisible fields. It starts to spin around the axis of the magnetic field, just like a top that's been given a gentle nudge. That's precession. But when the sphere becomes really small, quantum laws come into play.

Every 165 days, the giant planet dives toward its star, nearly grazing its fiery corona, then flies off into the icy void. This is TIC 241249530 b — an exoplanet with a record eccentricity of 0,94.

A tiny satellite, like a swimmer, cuts through invisible layers of gas in the bloated envelope of a red giant. Each orbit excites an acoustic wake — compression waves traveling through plasma.

In 1915, Albert Einstein and Wander Johannes de Haas demonstrated that when an iron rod is magnetized, it twists slightly — the angular momentum of electrons is transferred to the crystal lattice.

In a world where Reynolds numbers are minuscule, water turns into thick syrup, and the swimming tricks we know stop working. Here reigns the insidious scallop theorem: reciprocal motions produce no net displacement. Microorganisms found a way out: they grow polymer tails.

For decades, SETI has hunted for Dyson spheres — hypothetical shells that capture a star's light stars and re-radiate it in the infrared. But the cosmos remains silent. Perhaps an alien intelligence operates more elegantly: instead of collecting light, it tames the rotation of a sun, like a giant flywheel.

Two thousand years ago, a brilliant beacon shone in the constellation Eridanus, recorded in the registers of ancient astronomers. Hipparchus in 129 BCE noted it as a first-magnitude star, Ptolemy confirmed its brightness in the Almagest, and the Persian scholar Al-Sufi still saw it among the brightest in 964.

At the heart of a warp drive lies Einstein's idea that massive bodies curve spacetime — the very stage on which all cosmic events unfold. Picture a bubble of such curved spacetime. Inside it, the ship floats without any G-forces, like a passenger in an airplane cabin who doesn't feel the headwind.

The cosmic vacuum is not emptiness but a living ocean: its energy swells and subsides, echoing the expansion. Like a lunar tide, vacuum density sensitively responds to Hubble’s tempo — the conductor’s baton of the universe.

A tellurium crystal resembles a tiny spiral staircase: its atoms are twisted into a helix. When heat runs through such a crystal, it is carried not by electrons but by sound waves — vibrations of the lattice itself. These waves don't just push back and forth; they also rotate around their axis like a spinning top.

A heavy atomic nucleus of californium-252 can spontaneously split into two large fragments — much like a water droplet bursting apart. But inside such a droplet, quantum laws are at play, and each fragment acquires its own rotation — a spin.

A tiny magnet levitates in a magnetic trap, like a weightless needle. Its magnetized axis is like a stubborn compass needle that is prevented from turning. An invisible wall rises before it. But in the quantum world, particles can seep through barriers — this trick is called tunneling.

Sugar dissolves in tea, and then with a single motion gathers back into the spoon. In an ordinary kitchen, you won't see that — viscosity and disorder get in the way. But in the world of ultra-slow motions, where inertia vanishes, such tricks become reality.

A hot spoon in a cup of tea — heat runs along the metal from the hot end to the cold one. Textbooks describe this process as atoms jiggling and passing on their jolts to each other. But atoms don't just jiggle: they also spin, like tiny tops. Until now, physicists had no common language to describe both motions at once. The authors of the work built such a language.

Light isn't just straight rays; it's electromagnetic waves that can twist through space like a pair waltzing. Physicists call their total twist orbital angular momentum, and for a long time it was thought to obey the conservation law — a fundamental principle that follows from the symmetries of nature discovered by Emmy Noether.

Water in a circular hose, pumped around by a pump, won't stop even if you pinch one section: the flow finds a detour and keeps going around. That's roughly how some parts of our circulatory system are arranged — not as single pipes but as closed loops. Scientists built a computer model of blood flow and compared two scenarios: an open vessel and a closed loop.

The pulsar in the Crab Nebula blinks like a lighthouse: every 33 milliseconds it sends out a radio pulse, and it does so with the precision of atomic clocks. But sometimes its rotation stumbles: the star suddenly speeds up slightly, as if something inside it is shifting.

An ordinary top spun on a table slows down smoothly: friction with the air and the surface gradually eats away its energy. But if a top levitates in a magnetic field and barely touches anything, its rotation can behave surprisingly capriciously.

Spacetime at ultra-short distances resembles a digital screen: it's not smooth but made of tiny 'pixels.' This minimum length was calculated by Max Planck, and Heisenberg's uncertainty principle explains why the world cannot be continuous: precise measurement always…

A century ago, quantum mechanics gave the world a neat picture: a particle rotating around a point can only have certain discrete amounts of angular momentum, integer multiples of Planck's constant. This rule seemed as solid as the law of gravity, and it followed from simple algebraic arguments.

Think of a reliable container instead of a fragile test tube: that's the shift from trapping chemically reactive radicals to holding stable molecules. Until now, magneto-optical traps have only worked with particles that are eager to react at the first collision.

The speedometer needle in a car shows how fast the wheels are spinning. The climate system also has rotation, but it is invisible: it happens in state space, where each point is a combination of ocean temperature, the depth of the warm layer, and other parameters.