An object is in equilibrium when it is not accelerating and not rotating. Two conditions must both be satisfied.
The two conditions
- The resultant force on the object is zero (no linear acceleration).
- The resultant moment about any point is zero (no rotational acceleration).
Condition 1 alone keeps the object from accelerating in a straight line. Condition 2 alone keeps it from starting to rotate. Both are needed for complete equilibrium.
Example: a balanced see-saw
A see-saw with two children balanced at rest satisfies both conditions:
- The upward force from the pivot equals the combined weight of the children and the see-saw (zero resultant force).
- The clockwise moments equal the anticlockwise moments about the pivot (zero resultant moment).
Example: a ladder against a wall
A ladder leaning against a smooth wall in equilibrium has:
- Vertical forces balanced: weight of ladder = normal contact force from the ground.
- Horizontal forces balanced: friction at the ground = normal contact force from the wall.
- Moments balanced about any point (usually taken about the base to eliminate unknown friction and normal forces at that point).
Common errors and how to correct them
Stating only one condition. Both conditions are needed. An object can have zero resultant force but still rotate (like a pair of equal and opposite forces separated by a distance, called a couple).
Confusing equilibrium with “at rest.” An object moving at constant velocity in a straight line with no rotation is also in equilibrium.
How to apply this in an exam
When asked for conditions of equilibrium, always state both: resultant force = 0 and resultant moment about any point = 0. For calculation questions, apply the principle of moments for condition 2 and resolve forces for condition 1.
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