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The total (mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = ma, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e. its ...
Proper acceleration (the acceleration 'felt' by the object being accelerated) is the rate of change of rapidity with respect to proper time (time as measured by the object undergoing acceleration itself). Therefore, the rapidity of an object in a given frame can be viewed simply as the velocity of that object as would be calculated non ...
Even if we pick units where =, the magnitude of the proper acceleration will depend on our choice of units: for example, if we use units of light-years for distance, (or ) and years for time, (or ), this would mean = light year/year 2, equal to about 9.5 meters/second 2, while if we use units of light-seconds for distance, (or ), and seconds ...
Born rigidity is satisfied if the orthogonal spacetime distance between infinitesimally separated curves or worldlines is constant, [7] or equivalently, if the length of the rigid body in momentary co-moving inertial frames measured by standard measuring rods (i.e. the proper length) is constant and is therefore subjected to Lorentz contraction in relatively moving frames. [8]
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame.
So, calculations made in both frames show that the thread will break; in S′ due to the non-simultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread. In the following, the rest length [3] or proper length [4] of an object
acceleration due to gravity The acceleration on an object caused by the force of gravitation. accelerometer An instrument used to measure the proper acceleration of a body irrespective of other forces. acoustics The branch of physics dealing with the production, transmission, and effects of sound. adhesion adhesion is what makes things stick ...
The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μ α) and of declination (μ δ). Their combined value is computed as the total proper motion (μ). [2] [3] It has dimensions of angle per time, typically arcseconds per year or milliarcseconds ...