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Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative ...
In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [13] : 1112. The force in the equation is not the force the object exerts. Replacing momentum by mass times velocity, the law is also written more famously as.
Planck–Einstein equation and de Broglie wavelength relations. P = ( E/c, p) is the four-momentum, K = (ω/ c, k) is the four-wavevector, E = energy of particle. ω = 2π f is the angular frequency and frequency of the particle. ħ = h /2π are the Planck constants. c = speed of light.
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 ...
Bernoulli's equation. pconstant is the total pressure at a point on a streamline. Euler equations. ρ = fluid mass density. u is the flow velocity vector. E = total volume energy density. U = internal energy per unit mass of fluid. p = pressure. ⊗ {\displaystyle \otimes }
Equations for a falling body. 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 ...
Download as PDF; Printable version; ... and expressed by the vector analysis formula ... (where v is the free stream fluid velocity and t is time).
The Frenet–Serret formulas are frequently introduced in courses on multivariable calculus as a companion to the study of space curves such as the helix. A helix can be characterized by the height 2π h and radius r of a single turn. The curvature and torsion of a helix (with constant radius) are given by the formulas.
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