Dimensions of mass M = L³ / T²
Given
the principle that the same physical quantity will always have the same
dimensions (a surface, for example, will always be defined by the square
of its length, L² ; linear speed will always be defined as the relationship
between distance and time, L / T), the force resulting from the acceleration
of mass and the force resulting from the attraction between masses should
always have the same dimensions. According to the equivalence principle
both forces are considered identical.
It follows that the Newton constant will have no dimension and that mass will not be a fundamental quantity and will have as its dimensions L³/T². The unit of mass will become m³ / s² and 1kg of mass will be 8,3868 10^-10 m³ / s² (see Appendix 2). Since the
unit of mass is (metre)³ / (second)² , or ( m³ / s²
), the Newton constant will be 1/4 p A certain
electric charge will give out measurable force when interacting with another
charge or with an electric field. When combining two complex quantities
(i² = -1) we obtain measurable quantities. For example, the electric
charge (complex quantity) situated in an electric field (also a complex
quantity) will result in force (real quantity). This way of seeing things allows us to establish a narrow relationship between classical mechanics and electromagnetism.
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