Search results
Results from the WOW.Com Content Network
The kinetic energy equations are exceptions to the above replacement rule. The equations are still one-dimensional, but each scalar represents the magnitude of the vector, for example, = + +. Each vector equation represents three scalar equations.
The equation for universal gravitation thus takes the form: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses , and G is the gravitational constant .
A differential equation of motion, usually identified as some physical law (for example, F = ma), and applying definitions of physical quantities, is used to set up an equation to solve a kinematics problem. Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a set of ...
The solution of the equations is a flow velocity.It is a vector field—to every point in a fluid, at any moment in a time interval, it gives a vector whose direction and magnitude are those of the velocity of the fluid at that point in space and at that moment in time.
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Newton's law of motion for a particle of mass m written in vector form is: = , where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of the particle, given by: = , where r is the position vector of the particle (not to be confused with radius, as ...
This is simplest to express for the case of a single point mass, in which is a function (,), and the point mass moves in the direction along which changes most steeply. In other words, the momentum of the point mass is the gradient of S {\displaystyle S} : v = 1 m ∇ S . {\displaystyle \mathbf {v} ={\frac {1}{m}}\mathbf {\nabla } S.}
This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [1] [2] [3] and that the particles are free.