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How does statics explain why an object can remain at rest?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

In physics, statics explains that an object remains at rest when it is in a state of equilibrium. For a rigid body to maintain this state, two fundamental conditions must be met:12

Net Force is Zero: The sum of all forces acting on the body must be zero, meaning all applied forces are perfectly balanced by counterforces.12
Net Torque is Zero: There must be no net torque acting on the body, ensuring there is no tendency for it to rotate about any axis.12

Statics assumes that bodies are perfectly rigid, meaning their dimensions do not change under load. When these equilibrium conditions are satisfied, the body remains at rest because there is no unbalanced force or torque to alter its state of motion, consistent with the law of inertia. If a body is subjected to a combination of forces, it can be brought into equilibrium by applying an equilibrant—a force equal and opposite to the resultant of all other forces acting on the object.123