Editing Torsion spring (section)

==Torsion balance==
[[File:Bcoulomb.png|thumb|right|Drawing of Coulomb's torsion balance. From Plate 13 of his 1785 memoir.]]
[[File:ConstantOfGravitation 003.jpg|thumb|Torsion balance used by [[Paul R. Heyl]] in his measurements of the gravitational constant G at the U.S. [[NIST|National Bureau of Standards]] (now NIST) between 1930 and 1942.]]

The '''torsion balance''', also called '''torsion pendulum''', is a scientific apparatus for measuring very weak forces, usually credited to [[Charles-Augustin de Coulomb]], who invented it in 1777, but independently invented by [[John Michell]] sometime before 1783.<ref>{{Citation|last2=McCormmach|first2=R.|author2-link=Russell McCormmach|last1=Jungnickel|first1=C.|author1-link=Christa Jungnickel|title=Cavendish|year=1996|publisher=American Philosophical Society|url=https://books.google.com/books?id=EUoLAAAAIAAJ|isbn=0-87169-220-1|pages=335–344}}</ref>  Its most well-known uses were by Coulomb to measure the [[electrostatic force]] between charges to establish [[Coulomb's Law]], and by [[Henry Cavendish]] in 1798 in the [[Cavendish experiment]]<ref>{{Citation|last=Cavendish|first=H.|year=1798|chapter=Experiments to determine the Density of the Earth|editor-last=MacKenzie|editor-first=A.S.|publication-date=1900|title=Scientific Memoirs, Vol.9: The Laws of Gravitation|url=https://books.google.com/books?id=O58mAAAAMAAJ|publisher=American Book Co.|pages=59–105}}</ref> to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the [[gravitational constant]].

The torsion balance consists of a bar suspended from its middle by a thin fiber.  The fiber acts as a very weak torsion spring.  If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or torque of the fiber balances the applied force.  Then the magnitude of the force is proportional to the angle of the bar.  The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar.

In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread.  The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it.  The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument.  By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls.  Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as [[Coulomb's law]].

To measure the unknown force, the [[Torsion spring#Torsion coefficient|spring constant]] of the torsion fiber must first be known.  This is difficult to measure directly because of the smallness of the force.  Cavendish accomplished this by a method widely used since: measuring the [[Resonance|resonant vibration period]] of the balance.  If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a [[harmonic oscillator]], at a frequency that depends on the [[moment of inertia]] of the beam and the elasticity of the fiber.  Since the inertia of the beam can be found from its mass, the spring constant can be calculated.

Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir, ''Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal &c''.  This led to its use in other scientific instruments, such as [[galvanometer]]s, and the [[Nichols radiometer]] which measured the [[radiation pressure]] of light.  In the early 1900s gravitational torsion balances were used in petroleum prospecting.  Today torsion balances are still used in physics experiments.  In 1987, gravity researcher A. H. Cook wrote:

<blockquote>The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by Michell and its use by Cavendish.  It has been the basis of all the most significant experiments on gravitation ever since.<ref>{{Citation|last=Cook|first=A. H.|chapter=Experiments in Gravitation|editor-last=Hawking|editor-first=S.W. |editor2=Israel, W.|title=Three Hundred Years of Gravitation|publication-date=1987|publisher=Cambridge University Press|isbn=0-521-34312-7|page=52|year=1987}}</ref></blockquote>In the [[Eötvös experiment]], a torsion balance was used to prove the ''[[equivalence principle]]'' - the idea that inertial mass and gravitational mass are one and the same.