nx_torque.nx

nx_torque.nx -- 3D torque vector primitive (rotational analog of nx_force). Layer 1 physics per [[feedback-engineering-sciences-bits-up-3d-print-first]]. Key composition demo: nx_torque_from_position_force computes τ = r × F via nx_force_cross + bit-cast. This is the FIRST substrate primitive that BUILDS a different-type primitive from COMPOSING another -- demonstrating the cross-primitive composition pattern the engineering sciences arc relies on. Unit convention: Q14 Newton-metres (N·m). 1 Q14 unit = 1/16384 N·m = 61 µN·m. Range ±5e14 N·m -- vastly exceeds any engineering use (NEMA-23 stepper holding torque ~1 N·m; jet engine thrust ~10⁶ N·m). IMPORTANT unit-pairing convention for the cross product: position r in metres (Q14) force F in Newtons (Q14) result τ in N·m (Q14) Slicer/printer callers operate in mm by default. Convert position from Q14 mm to Q14 m by dividing by 1000 (integer division loses sub-µm precision, acceptable for motor-sizing calcs). Or use millimetric variant queued for v2. Composes: nx_force (force vector input + reuses cross product) nx_isqrt (magnitude via Q28 sum-of-squares) nx_i128 / nx_muldiv_i64 (overflow protection for large-scale ops) Future v2 enhancements: nx_torque_from_position_force_mm (mm-position variant for slicer) nx_torque_required_for_angular_accel (τ = Iα, needs nx_inertia) nx_torque_at_lever (planar 2D case for simple analyses) license_tier: ORIGINAL