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An actuator disk accelerating a fluid flow from right to left. In fluid dynamics, momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor, by W.J.M. Rankine (1865), [1] Alfred George Greenhill (1888) and Robert Edmund Froude (1889).
The Kaufmann–Bucherer–Neumann experiments measured the dependence of the inertial mass (or momentum) of an object on its velocity. The historical importance of this series of experiments performed by various physicists between 1901 and 1915 is due to the results being used to test the predictions of special relativity.
To explain the difference between theory and experiment, the two striking balls must have at least ≈ 10 μm separation (given steel, 100 g, and 1 m/s). This shows that in the common case of steel balls, unnoticed separations can be important and must be included in the Hertzian differential equations, or the simple solution gives a more ...
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
In the theory of special relativity, physical quantities are expressed in terms of four-vectors that include time as a fourth coordinate along with the three space coordinates. These vectors are generally represented by capital letters, for example R for position. The expression for the four-momentum depends on how the coordinates are expressed ...
Mass, velocity, momentum, and energy of electrons have been measured in different ways in those experiments, all of them confirming relativity. [13] They include experiments involving beta particles, Compton scattering in which electrons exhibit highly relativistic properties and positron annihilation.
The momentum theory or disk actuator theory – a theory describing a mathematical model of an ideal propeller – was developed by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and Robert Edmund Froude (1889). The propeller is modelled as an infinitely thin disc, inducing a constant velocity along the axis of rotation.
The Stern–Gerlach experiment was the first direct evidence of angular-momentum quantization in quantum mechanics, [23] and it strongly influenced later developments in modern physics: In the decade that followed, scientists showed using similar techniques, that the nuclei of some atoms also have quantized angular momentum. [20]