Search results
Results from the WOW.Com Content Network
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. [4] It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. The equation for universal gravitation thus takes the form:
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
In analytical mechanics (particularly Lagrangian mechanics), generalized forces are conjugate to generalized coordinates.They are obtained from the applied forces F i, i = 1, …, n, acting on a system that has its configuration defined in terms of generalized coordinates.
This is because the gravitational force is an extremely weak force as compared to other fundamental forces at the laboratory scale. [d] In SI units, the CODATA-recommended value of the gravitational constant is: [1] = 6.674 30 (15) × 10 −11 m 3 ⋅kg −1 ⋅s −2. The relative standard uncertainty is 2.2 × 10 −5.
The force, therefore, is related directly to the difference in potential energy between two different locations in space, [56] and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area.
The two forms of Gauss's law for gravity are mathematically equivalent. The divergence theorem states: ∮ ∂ V g ⋅ d A = ∫ V ∇ ⋅ g d V {\displaystyle \oint _{\partial V}\mathbf {g} \cdot d\mathbf {A} =\int _{V}\nabla \cdot \mathbf {g} \,dV} where V is a closed region bounded by a simple closed oriented surface ∂ V and dV is an ...
In general I is an order-2 tensor, see above for its components. The dot · indicates tensor contraction. Force and Newton's 2nd law: Resultant force acts on a system at the center of mass, equal to the rate of change of momentum: