Equilibrium happens when all the forces pushing or pulling an object cancel each other out, leaving the object perfectly still.

What is Equilibrium?

In physics, a particle is in equilibrium when it stays at rest or keeps moving in a straight line at a steady speed. For this to happen, the total force acting on the particle must be zero. Imagine a toy hanging from a string; gravity pulls it down, but the string pulls it up with the exact same amount of force. Because these two forces are equal and opposite, the toy does not move.

Lami's Theorem Explained

Lami's theorem is a special rule used when exactly three forces act on a single point to keep it in equilibrium. It states that each force is proportional to the sine of the angle between the other two forces. If we have three forces—let’s call them P, Q, and R—and the angles opposite to them are α, β, and γ, the formula is:

P / sin(α) = Q / sin(β) = R / sin(γ)

In this equation, sine is a mathematical tool used to relate the angles of a triangle to its sides. This theorem makes it easy to calculate unknown forces if you know the angles and at least one of the forces.

Conditions for Lami's Theorem

• The forces must all act on the same point.
• The object must be in equilibrium, meaning the net force is zero.
• The three forces must lie on the same flat surface (coplanar).

Real-World Examples

Think about a picture frame hanging on a wall held by two strings tied at the same point. The weight of the frame pulls down, while the two strings pull up and to the sides. These three forces meet at a single point. You can use Lami's theorem to find out exactly how much tension or pull is in each string just by measuring the angles between them. Engineers use this same logic to design bridges and cranes so they can safely hold heavy weights without falling.