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A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
These are known as the Navier–Stokes equations. [35] The momentum balance equations can be extended to more general materials, including solids. For each surface with normal in direction i and force in direction j, there is a stress component σ ij. The nine components make up the Cauchy stress tensor σ, which includes both pressure and shear.
There are different derivations for the variable-mass system motion equation, depending on whether the mass is entering or leaving a body (in other words, whether the moving body's mass is increasing or decreasing, respectively). To simplify calculations, all bodies are considered as particles. It is also assumed that the mass is unable to ...
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc 2 relates total energy E to the (total) relativistic mass m (alternatively denoted m rel or m tot), while E 0 = m 0 c 2 relates rest energy E 0 to (invariant) rest mass m 0. Unlike either of those equations, the energy ...
All acceleration requires an exchange of momentum, which can be thought of as the "unit of movement". Momentum is related to mass and velocity, as given by the formula P = mv, where P is the momentum, m the mass, and v the velocity. The velocity of a body is easily changeable, but in most cases the mass is not, which makes it important.
Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r from the axis.