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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity.Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
where t = t(n) is called the surface traction, integrated over the surface of the body, in turn n denotes a unit vector normal and directed outwards to the surface S. Let the coordinate system ( x 1 , x 2 , x 3 ) be an inertial frame of reference , r be the position vector of a point particle in the continuous body with respect to the origin of ...
If the number of constraints in the system is C, then each constraint has an equation f 1 (r, t) = 0, f 2 (r, t) = 0,..., f C (r, t) = 0, each of which could apply to any of the particles. If particle k is subject to constraint i, then f i (r k, t) = 0. At any instant of time, the coordinates of a constrained particle are linked together and ...
At a low speed (v ≪ c), the relativistic kinetic energy is approximated well by the classical kinetic energy. To see this, apply the binomial approximation or take the first two terms of the Taylor expansion in powers of v 2 {\displaystyle v^{2}} for the reciprocal square root: [ 14 ] : 51
[2] [3] It is also known as the Kolmogorov forward equation, after Andrey Kolmogorov, who independently discovered it in 1931. [4] When applied to particle position distributions, it is better known as the Smoluchowski equation (after Marian Smoluchowski ), [ 5 ] and in this context it is equivalent to the convection–diffusion equation .
A Magic Triangle image mnemonic - when the terms of Ohm's law are arranged in this configuration, covering the unknown gives the formula in terms of the remaining parameters. It can be adapted to similar equations e.g. F = ma, v = fλ, E = mcΔT, V = π r 2 h and τ = rF sinθ.