Force
In special relativity, Newton's second law does not hold in its form F = ma, but it does if it is expressed as
where p is the momentum as defined above () and "m" is 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. Thus, the force is given by
Carrying out the derivatives gives
which, taking into account the identity , can also be expressed as
If the acceleration is separated into the part parallel to the velocity and the part perpendicular to it In physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, acceleration is the rate at which something speeds up or slows down. However, as a vector quantity, acceleration is also the, one gets
Consequently in some old texts, γ3m is referred to as the longitudinal mass, and γm is referred to as the transverse mass, which is the same as 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,. See mass in special relativity 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,.
For the four-force In general relativity the relation between four-force, and four-acceleration remains the same, but the elements of the four-force are related to the elements of the four-momentum through a covariant derivative with respect to proper time, see below Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies".
<<Table of Contents Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies" | Next>> | Show All>>
