Conditions for Equilibrium
Simple Explanation
An object is in complete (static) equilibrium only when it satisfies TWO conditions at once: the net force acting on it is zero (so it does not accelerate linearly), and the net torque acting on it is zero (so it does not begin rotating).
Why Do We Need It?
Checking BOTH conditions is essential — an object can have zero net force but still start rotating if there's a net torque, or vice versa, so a complete equilibrium analysis always needs both.
Formula
Conditions for Equilibrium
ΣF = 0 and Στ = 0
An object is in complete (static) equilibrium only when both the net force AND the net torque acting on it are zero — the first condition prevents linear acceleration, the second prevents rotational (angular) acceleration.
- ΣF
- — The vector sum of all forces acting on the object
- Στ
- — The sum of all torques acting on the object, about any chosen pivot
When to use it: Use to analyse any object that is not accelerating linearly or rotationally — e.g. a beam resting on supports, or a ladder leaning against a wall.
Worked Example
Balancing a seesaw
A 300 N child sits 1.5 m from the pivot of a seesaw. Where must a 450 N adult sit on the other side for balance (net torque = zero)?
Why Does This Work?
Setting the sum of forces to zero prevents any net push in any direction (preventing linear acceleration); separately setting the sum of torques (about any chosen pivot) to zero prevents any net turning effect — an object satisfying both simply stays still (or moves at constant velocity without rotating), which is the definition of complete equilibrium.
Real-Life Example
A ladder leaning safely against a wall
A ladder leaning against a wall must not slide (net force = 0) or tip over (net torque = 0) to be safe to climb.
Engineers and safety guidelines analyse both the force balance (friction at the base versus the ladder's weight and the wall's push) and the torque balance (about the base) to determine the safe angle and conditions for the ladder to remain in equilibrium.
Practice
Why does an object need BOTH ΣF = 0 AND Στ = 0 to be in complete equilibrium?
MediumCommon mistake
Checking only the force balance (ΣF = 0) and assuming that's sufficient for equilibrium — an object can have zero net force while still experiencing a net torque (for example, two equal, opposite forces applied at different points, forming a 'couple'), which would still cause rotation.
Quick Review
- Complete equilibrium requires BOTH ΣF = 0 and Στ = 0.
- ΣF = 0 prevents linear acceleration; Στ = 0 prevents rotation.
- Torque can be summed about any chosen pivot point.