Fast-moving objects and systems of objects
If you push on an object in the direction of motion, it gains momentum and it gains energy. But if the object is already travelling near the speed of light The speed of light is a fundamental physical constant of spacetime, the speed at which electromagnetic radiation, including visible light, travels in free space. It is an upper bound on the rate of transfer of matter and information between places. The speed of light is usually denoted by the symbol c, it can't move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase, but its speed approaches a constant value—the speed of light. This means that in relativity the momentum of an object cannot be a constant times the velocity, nor is the kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude given by ½mv2.
The relativistic mass The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. However, the more general invariant mass may also be applied to systems of particles in relative motion, is defined as the ratio of the momentum of an object to its velocity, and it depends on the motion of the object. If the object is moving slowly, the relativistic mass is nearly equal to the rest mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass. As the object approaches the speed of light, the relativistic mass becomes infinite, because the momentum becomes infinite.
The relativistic mass is always equal to the total energy divided by c2. Because the relativistic mass is exactly proportional to the energy, relativistic mass and relativistic energy are nearly synonyms; the only difference between them is the units. If length and time are measured in natural units In physics, natural units are physical units of measurement defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1, the speed of light is equal to 1, and even this difference disappears. Then mass and energy have the same units and are always equal, so it is redundant to speak about relativistic mass, because it is just another name for the energy. This is why physicists usually reserve the useful short word "mass" to mean rest-mass.
For things made up of many parts, like a nucleus The nucleus of an atom is the very dense region, consisting of nucleons , at the center of an atom. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus, with a very small contribution from the orbiting electrons, planet A planet , is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.[a], or star A star is a massive, luminous ball of plasma that is held together by gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth. Other stars are visible in the night sky, when they are not outshone by the Sun. Historically, the most prominent stars on the celestial sphere were grouped together into, the relativistic mass is the sum of the relativistic masses of the parts, because energy adds up. In some cases, however, the parts include fields of force, and if the fields are attractive, they contribute a negative amount to the mass-energy. For example, the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up. The amount by which it is smaller is the energy required to break up the nucleus into individual protons and neutrons. Similarly, the mass of the solar system is slightly less than the masses of sun and planets individually, since the gravitational field is attractive.
The relativistic mass of a moving object is bigger than the relativistic mass of an object that isn't moving, because a moving object has extra kinetic energy. The rest mass of an object is defined as the mass of an object when it is at rest, so that the rest mass is always the same independent of the motion of the observer: it is the same in all inertial frames In physics, an inertial frame of reference is a reference frame, tied to the state of motion of an observer, with the property that each physical law portrays itself in the same form in every inertial frame. The contrasting case is the set of non-inertial frames, in which the laws of physics change from frame to frame, and the usual forces.
For a system of particles going off in different directions, the invariant mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the is the analog of the rest mass, defined as the total energy (divided by c2) in the center of mass frame A center of momentum frame of a system is any inertial frame in which the center of mass is at rest (has zero velocity). Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame (a velocity and a direction). Thus "center of momentum" already means "center of momentum frame", where the total momentum is zero.
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