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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.
is the torque exerted by the spring in newton-meters, and is the angle of twist from its equilibrium position in radians κ {\displaystyle \kappa \,} is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient , torsion elastic modulus , rate , or just spring constant , equal to the change in torque ...
In 1676 British physicist Robert Hooke postulated Hooke's law, which states that the force a spring exerts is proportional to its extension. On March 8, 1850, John Evans, Founder of John Evans' Sons, Incorporated, opened his business in New Haven, Connecticut, manufacturing flat springs for carriages and other vehicles, as well as the machinery ...
This relationship is known as Hooke's law. A geometry-dependent version of the idea [a] was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", [5] [6] a linear relationship commonly referred to as Hooke's law.
In physics and mechanics, torque is the rotational analogue of linear force. [1] It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
Pulling the spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of force can be determined by multiplying the spring constant, characteristic of the spring, by the amount of stretch, also known as Hooke's Law. Another example is of a pendulum.
However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Mathematically, F = − k x , {\displaystyle \mathbf {F} =-k\mathbf {x} ,} where F is the restoring elastic force exerted by the spring (in SI units: N ), k is the spring constant ( N ·m −1 ), and x is the ...
This theory, based on the ... and Hooke's law for springs. ... Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for ...