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In the inertial frame, the differential equation is not always helpful in solving for the motion of a general rotating rigid body, as both I in and ω can change during the motion. One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant.
Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed.
The inertial frames may move in all possible relative forms of uniform motion. There is a universal, or absolute, notion of elapsed time. Two inertial frames are related by a Galilean transformation. In all inertial frames, Newton's laws, and gravity, hold. In comparison, the corresponding statements from special relativity are as follows:
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
An observational frame (such as an inertial frame or non-inertial frame of reference) is a physical concept related to state of motion. A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations. [3]
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.
The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames. Newton's gravitational constant G is a dynamical field. An isolated body in otherwise empty space has no inertia. Local inertial frames are affected by the cosmic motion and distribution of matter.
1. First postulate (principle of relativity) The laws of physics take the same form in all inertial frames of reference.. 2. Second postulate (invariance of c) . As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.