Q.What are concurrent forces? State Lami's theorem.

Step 1. Concurrent forces are a set of forces whose lines of action all pass through one common point; they need not lie in the same plane, though when they do, they are called coplanar and concurrent.

Step 2. Lami's theorem applies to three coplanar, concurrent forces $\vec F_1,\vec F_2,\vec F_3$ acting on a point that is in equilibrium (net force zero).

Step 3. The theorem states that the magnitude of each force is proportional to the sine of the angle between the OTHER two forces, with the same constant of proportionality for all three: $F_1\propto\sin\alpha$, $F_2\propto\sin\beta$, $F_3\propto\sin\gamma$, where $\alpha$ is the angle between $\vec F_2$ and $\vec F_3$ (opposite $\vec F_1$), and similarly for the others.

Step 4. Combining these gives the standard form $\dfrac{F_1}{\sin\alpha}=\dfrac{F_2}{\sin\beta}=\dfrac{F_3}{\sin\gamma}$.

Step 5. This is very useful for bodies held in static equilibrium by exactly three forces (e.g. a swing hanging from two chains, or a sling shot's two strings and applied force), directly relating the unknown tensions to the known angles without resolving into components.

Identify the three concurrent, coplanar forces at the equilibrium point and match each force with the angle between the OTHER two.

• Matching a force with the angle it makes with the other forces, instead of the angle BETWEEN the other two.
• Applying Lami's theorem when more than three forces act (it is valid strictly for exactly three concurrent coplanar forces).