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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
,
Lami There is no such page as “Lami”. Lami may refer to: People * Lami (name), list of people with the name. Places * Lami, Fiji, town * Lami (Open Constituency, Fiji) * Lami José Lutzenberger Biological Reserve * Lami, Porto Alegre, Brazil Oth ...
's theorem is an equation relating the magnitudes of three
coplanar In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. How ...
,
concurrent Concurrent means happening at the same time. Concurrency, concurrent, or concurrence may refer to: Law * Concurrence, in jurisprudence, the need to prove both ''actus reus'' and ''mens rea'' * Concurring opinion (also called a "concurrence"), a ...
and non-collinear vectors, which keeps an object in
static equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero ...
, with the angles directly opposite to the corresponding vectors. According to the theorem, :\frac=\frac=\frac where ''A'', ''B'' and ''C'' are the magnitudes of the three coplanar, concurrent and non-collinear vectors, V_A, V_B, V_C, which keep the object in static equilibrium, and ''α'', ''β'' and ''γ'' are the angles directly opposite to the vectors. : Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after
Bernard Lamy Bernard Lamy (15 June 1640 – 29 January 1715) was a French Oratorian, mathematician and theologian. Life Lamy was born in Le Mans, France. After studying there, he went to join the Maison d'Institution in Paris, and to Saumur thereafter. In ...
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Proof

As the vectors must balance V_A+V_B+V_C=0, hence by making all the vectors touch its tip and tail we can get a triangle with sides A,B,C and angles 180^o -\alpha, 180^o -\beta, 180^o -\gamma. By the law of sines then \frac=\frac=\frac. Then by applying that for any angle \theta, \sin (180^o - \theta) = \sin \theta we obtain \frac=\frac=\frac.


See also

*
Mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is ze ...
*
Parallelogram of force The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object. When more than two forces are involved, the geometry is no longer parallelogrammatic, but the same principles apply. Forces, ...
*
Tutte embedding In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free straight-line embedding with the properties that the outer face is a convex polygon and ...


References


Further reading

* R.K. Bansal (2005). "A Textbook of Engineering Mechanics". Laxmi Publications. p. 4. . * I.S. Gujral (2008). "Engineering Mechanics". Firewall Media. p. 10. {{ISBN, 978-81-318-0295-3 Statics Physics theorems