Newtonian Mechanics (NM18–NM30)

13 operators covering classical mechanics — Newton’s laws, gravitation, energy conservation, momentum, angular momentum, and simple harmonic motion.

NM18 — First Law (Inertia)

∑F = 0 ⇒ v = const

A body at rest stays at rest, and a body in motion stays in uniform motion, unless acted upon by a net external force.

NM19 — Second Law

F = ma

Net force equals mass times acceleration. The most frequently invoked operator in multi-scale computations.

NM20 — Third Law

F&sub1;&sub2; = −F&sub2;&sub1;

Every action has an equal and opposite reaction.

NM21 — Universal Gravitation

F = G m&sub1; m&sub2; / r²

Gravitational force between two masses. Benchmark: Earth-Moon = 1.98 × 10²&sup0; N (verified to ≤0.1% in v1.1.3).

NM22 — Work

W = F · d

Work done by a force over a displacement. Scalar product of force and distance vectors.

NM23 — Kinetic Energy

KE = ½ mv²

Energy of motion. Together with NM24, forms the energy conservation pair (NM25).

NM24 — Potential Energy

PE = mgh

Gravitational potential energy near Earth’s surface.

NM25 — Energy Conservation

KE + PE = const

In a closed system with conservative forces, total mechanical energy is conserved.

NM26 — Momentum

p = mv

Linear momentum — mass times velocity.

NM27 — Momentum Conservation

∑p_init = ∑p_final

In the absence of external forces, total momentum is conserved. Essential for collision computations.

NM28 — Angular Momentum

L = r × p

Rotational analogue of linear momentum. Cross product of position and momentum vectors.

NM29 — Torque

τ = r × F

Rotational force — cross product of lever arm and applied force.

NM30 — Simple Harmonic Motion

F = −kx,   x(t) = A cos(ωt + φ)

Restoring force proportional to displacement produces oscillatory motion. Foundation of wave mechanics and HulyaPulse timing.

API Usage

Call any operator via the Compute API:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer zk_live_..." \
  -d '{"query": "Gravitational force between Earth and Moon", "operators": ["NM21, KO42"]}'

The 7-step wizard protocol selects the right operators automatically when you omit the operators field. KO42 is always included.