Torque

Torque τ is the rotational analog of force — measures the tendency of a force to rotate a body about an axis.

τ = r × F. Magnitude: τ = r·F·sin θ = F·r_perp = r·F_perp.

Units: N·m (same as energy units, but conceptually different — vector vs scalar).

Direction: perpendicular to plane of r and F (right-hand rule).

Rotational Newton's 2nd law: τ_net = I·α.

Equilibrium: a body is in mechanical equilibrium when Σ F = 0 AND Σ τ = 0 (both translational and rotational).

Couple: two equal-magnitude, opposite-direction forces with different lines of action — produces pure rotation (net F = 0 but τ ≠ 0).

Lever, wrench, door hinge — all use torque. Long lever arm = more rotational effect for same force.