For a long object with mass, gravity acts on every point, and so no matter what rotation axis is assumed, the force of gravity exerts a torque on the rest of the object. In the discussion of torque, the effect of the distance between a force and a rotation axis was described. However, because it is maintaining a constant velocity, it is not in static equilibrium.įor the forces on an object to be in equilibrium, the force of gravity on the object must be accounted for. In these formulas, is the linear velocity of the object, and is the angular velocity of the object.įor example, an airplane that is maintaining a fixed altitude and velocity has balanced forces acting on it, meaning that it is in equilibrium. Expressed in vector form, static equilibrium requires, An object in static equilibrium must have no linear or angular velocity. Static equilibrium requires an object to be at rest, both translationally and rotationally. Another set of conditions must be met for an object to be in static equilibrium.
It is in equilibrium both translationally and rotationally. These two conditions for equilibrium result in a system that has no tendency to accelerate linearly, or angularly. Expressed in vector form, the second condition is stated, This means that the sum of the torques must be zero, for any given axis on the object. The second condition for equilibrium is that the object must have no tendency to rotate. Expressed in vector form, the first condition is stated,įor this vector equation to be true, the sum of the magnitudes of the forces in each axis must be zero, The first condition for equilibrium is that the net external force is equal to zero. If the forces and torques that act on the ladder are not in equilibrium, the ladder may slide or fall.
The force of gravity acts on the ladder's center of mass, if the ladder is leaning against a wall there are forces of friction acting on the two ends, and a person climbing the ladder exerts an additional force. This not only applies to forces that act on the center of mass of the object, it also requires that the torques on the object are balanced.įor an extended object like a ladder, forces can act at multiple points. This requires that the effects of these forces are balanced. An object is in equilibrium when it is stationary, even though it is acted on by a number of forces.
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