Translational and rotational equilibrium

Repair the common break

Common misconception: Zero resultant force alone proves equilibrium.

Correct model: Equilibrium requires both zero resultant force and zero resultant torque, represented with a complete free-body model.

Worked transfer

For a uniform horizontal beam in equilibrium, first impose ΣFy = 0 to relate the support forces, then take moments about one support. Satisfying only the force equation still permits angular acceleration.

Guided practice

Explain why “Zero resultant force alone proves equilibrium.” fails. Then construct one example that correctly applies translational and rotational equilibrium.

Independent practice

A sign of weight 240 N hangs from a horizontal beam supported by a hinge and cable. State the two independent equilibrium conditions and choose a pivot that eliminates the hinge forces.

Return to the recorded repair plan when the explanation and application are secure enough to re-test.