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Tuesday, 5 April 2011

Inertial frames of reference

Inertial frame of reference, adapted from Wikipedia, the free encyclopedia

In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes time and homogeneously and isotropically, and in a time independent manner. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating.
Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). Physical laws take the same form in all inertial frames. In a non-inertial reference frame the laws of physics depend upon the acceleration of that frame of reference, and the usual physical forces must be supplemented by fictitious forces.
The motion of a body can only be described relative to something else - other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body (one having no external forces on it) is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary.
An intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form.òIn an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction.Newton's second law for a particle takes the form:

F = m a

with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form:

F' = m a'

which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms:

F' = F - 2m Ω x v'-m Ω x (Ω  x r')

where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol  x denotes the vector cross product, vector r' locates the body and vector v' is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). We assume  for the sake of simplicity that the angular velocity  is constant in magnitude and direction.
The extra terms in the force F′ are the "fictitious" forces for this frame. (The first extra term is the Coriolis force, the second the centrifugal force). These terms all have these properties: they vanish when Ω = 0; that is, they are zero for an inertial frame (which, of course, does not rotate).
All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.
In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force.
 The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space.
Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property.