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Try pushing a heavy door open right next to its hinge, and then push at the outer handle. Even if you push with the exact same effort, the door barely budges at the hinge because rotational motion depends on both force and distance.
In physics, torque (symbol Ο„\tau) measures the rotational effectiveness of a force and is defined as Ο„=rFsin⁑θ\tau = r F \sin\theta, where rr is the distance from the pivot point to where the force is applied, FF is the force magnitude, and ΞΈ\theta is the angle between the lever arm and the force vector.
Around 250 BCE, the Greek mathematician Archimedes discovered the law of the lever, famously claiming that with a long enough lever and a place to stand, he could move the entire Earth.
So how do civil engineers use torque to ensure bridges and tower cranes remain rock-solid without toppling over?

The Two Conditions of Static Equilibrium

For an extended rigid body to remain completely motionless in static equilibrium, it must satisfy two independent vector conditions simultaneously.
First, the net external force must be zero (Ξ£Fβƒ—=0\Sigma \vec{F} = \mathbf{0}), ensuring zero linear acceleration; second, the net external torque about any arbitrary pivot point must be zero (Στ⃗=0\Sigma \vec{\tau} = \mathbf{0}), preventing rotational acceleration.
When calculating torques caused by gravity, an object's entire weight can be treated as acting at a single point called the center of gravity.
What happens when supports are placed unevenly along a beam carrying a heavy load?

Worked Example: Beam with Overhang

A uniform 4.0Β m4.0\text{ m} structural beam of mass 50Β kg50\text{ kg} rests horizontally on two supports: Support A is at the left end (x=0Β mx = 0\text{ m}), and Support B is at x=3.0Β mx = 3.0\text{ m}. A 100Β kg100\text{ kg} crate sits on the overhanging right edge at x=4.0Β mx = 4.0\text{ m}. Let g=9.8Β m/s2g = 9.8\text{ m/s}^2.