Lami's theorem

(Redirected from Triangle of forces)

In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding forces. According to the theorem, screw hindi videos on youTube

${\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}={\frac {C}{\sin \gamma }}$ where A, B and C are the magnitudes of the three coplanar, concurrent and non-collinear forces, $F_{A},F_{B},F_{C}$ , which keep the object in static equilibrium, and α, β and γ are the angles directly opposite to the forces.

Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.

Proof

As the forces must balance $F_{A}+F_{B}+F_{C}=0$ , hence by making all the forces 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 sine rule,

${\frac {A}{\sin(180^{o}-\alpha )}}={\frac {B}{\sin(180^{o}-\beta )}}={\frac {C}{\sin(180^{o}-\gamma )}}$ $\therefore {\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}={\frac {C}{\sin \gamma }}.$ 