First, nuclear waste isn't 100% radioactive atoms. Much of it is radioactively contaminated material—normal materials that contain enough radioactive atoms to be considered hazardous. Second, nuclear reactors don't wait for radioactive materials to decay via spontaneous processes, the ones that are responsible for half-lives. Instead, they induce the radioactive decays using chain reactions. In a nuclear fission reactor, the spontaneous decay of one uranium or plutonium nucleus is used to induce decays in other uranium or plutonium nuclei. In this manner, huge fractions of the uranium or plutonium nuclei can be "used up" in only a few years. In fact, in a nuclear fission bomb, many or most of the uranium or plutonium nuclei are consumed in less than a millionth of a second because of these induced fissions. Half-life has almost nothing to do with a fission bomb. It becomes nuclear waste so fast you can't imagine it.
Gravity provides the energy source for a roller coaster and inertia is what keeps the roller coaster moving when the track is level or uphill. Once the roller coaster is at the top of the first hill and detaches from the lifting chain, the only energy it has is gravitational potential energy (and a little kinetic energy—the energy of motion). But once it begins to roll down the hill, its gravitational potential energy diminishes and its kinetic energy increases. Since kinetic energy is related to speed, they both increase together.
At the bottom of the first hill, the roller coaster has very little gravitational potential energy left, but it does have lots of kinetic energy. The roller coaster also keeps moving, despite the absence of gravitational potential energy. You can view its continued forward motion as either the result of having lots of kinetic energy or a consequence of having inertia. Inertia is a feature of everything in our universe—a tendency of all objects to keep doing what they're doing. If an object is stationary, it tends to remain station. If an object was moving forward at a certain speed, it tends to keep moving forward at a certain speed. Inertia tends to keep the roller coaster moving forward along the track at a certain speed, even when nothing is pushing on the roller coaster. While the roller coaster will slow down as it rises up the next hill, its inertia keeps it moving forward.
Because of the quantum physic that dominates the behaviors of tiny objects in our universe, electrons can't travel in every path you can imagine; they can only travel in one of the paths that are allowed by quantum physics—paths that are called orbitals in atoms and levels in solids. When a material is assembled out of its constituent atoms, those atoms bring with them both their electrons and their quantum orbitals. These orbitals merge and blend as the atoms touch and they shift to form bands of levels in the resulting solid. The electrons in this solid end up traveling in the levels with the lowest energies. Because of the Pauli exclusion principle, only one indistinguishable electron can travel in each level. Since there are effectively two types of electrons, spin-up and spin-down, only two electrons can travel in each level of the solid.
In a conductor, there are many unused levels available within easy reach of the electrons. If the electrons have to begin moving toward the left, in order to carry an electric current, some of the electrons that are in right-heading levels can shift into empty left-heading levels in order to let that current flow. But in an insulator, all of the easily accessible levels are filled and the electrons can't shift to other levels in order to carry current in a particular direction. While there are empty levels around, an electron would need a large increase in its energy to begin traveling in one of these empty levels. As a result, the electrons in an insulator can't carry an electric current.
It's about 235,000 miles (375,000 kilometers) away from the earth's surface. However, it's drifting about 1.3 inches (3.5 centimeters) farther away every year. That's because tides on the rotating earth gently pull the moon forward in its orbit as they slowly extract energy from the earth's rotation. Because of this transfer of energy from the earth's rotation to the moon's orbit, the moon is gradually slipping farther away from the earth.
The earth's rotational axis wobbles around in a circle once every 25,800 years because of torques (twists) exerted on it by the moon's gravity. The moon's gravity is able to twist the earth slightly because the earth isn't quite spherical. The earth's rotation causes it to bulge outward a little around its equator and it is this bulging that allows the moon to exert a torque on the earth.
I'm afraid that travel at or above light speed is simply impossible and that "warp speed" travel is just a Hollywood fantasy. Einstein's special relativity forbids objects with mass from reaching or exceeding the speed of light and even if there were some way to travel vast distances in less time than it would take light to cover those distances, but without actually traveling at light speed, such travel would violate some important principles of causality—you would be able to meet your own grandparents as children and that sort of thing.
One of the reasons that Hollywood ignores real physics so often is that real physics is almost wilder than fiction. Suppose that you decided to travel to a star 5 light-years away from the earth and that you have a starship that can almost reach the speed of light (another nearly impossible thing, but let's ignore that problem). If you travel to the star at almost the speed of light, make one loop around it, and head right back to earth, I will have aged 10 years while waiting for you to return. However, you will only have aged days or weeks, depending on just how close you came to the speed of light. During the trip, we will have disagreed on many physical quantities, particularly the times at which various events occurred and the distances between objects. The mixing of time and space that occur when two people move rapidly relative to one another would be so disorienting to movie or television viewers that Hollywood ignores or simplifies these effects.
The Ohio River is carrying water collected by vast areas surrounding the river and this accumulated volume of water is enough to raise the river's level by many feet. Similarly, if you collected all the rain water that accumulated on your yard and poured that water into a bathtub, the level of water in the bathtub would rise far more than 15 inches.
Airplanes travel faster from west to east in the United States. That's because the prevailing winds at out latitudes are eastward and they blow the airplane toward the east. When the airplane flies toward the east, it has a tail wind and travels faster with respect to the ground. When the airplane flies toward the west, it has a headwind and travels slower with respect to the ground.
Some rockets probably reach the speed of sound in a few hundred feet heading upward, so that reaching the speed of sound in 30,000 feet heading downward would be a simple task. In fact, if you dropped a highly aerodynamic object such as a rocket from 30,000 feet, it could reach the speed of sound even without any propulsion! Gravity alone will accelerate it to about 130% of the speed of sound.
The answer is a qualified no. Heat always flows from hotter objects to colder objects, so the solid can't get any hotter than the flame that's heating it. But this observation is stems from the laws of thermodynamics, particularly the second law of thermodynamics. Unlike Newton's laws of motion, which are rigid, inviolable laws that are never, even violated in our universe, the second law of thermodynamics is a statistical laws—it says that certain events are extremely unlikely but doesn't say that they are truly impossible. The flow of heat from hotter to colder is a statistical law, not a rigid mechanical law. So it is possible, although extraordinarily unlikely, that heat can flow from the 1770° C flame to the 1799° C solid and warm that solid all the way to 1800° C. However, for any reasonable sized solid (say, more than 10 atoms), the possibility of this occurring is going to be so unbelievably small as to be ridiculous. It's as unlikely as taken a crystal wineglass that has been crushed into dust and then dropping it on the floor and having the impact reassemble the wineglass into its original pristine form. The laws of motion don't forbid such as fantastic result, but it sure would be unlikely. I've tried it several times myself, without success. But then, you're not going to be able to melt your solid with a not-hot-enough flame, either. You'd have to wait a few ages of the universe just to have that solid climb a tiny fraction of a degree above the temperature of the flame. For 20 degrees... forget it.