F = ma is the foundation of dynamics. 1 newton accelerates 1 kg at 1 m/s². Every force you feel is mass resisting acceleration.

• 1 N = 1 kg·m/s²
• Double force → double acceleration
• Force is a vector (has direction)
• Net force determines motion

Weight is gravitational force: W = mg. Your mass is constant, but weight changes with gravity. On Moon, you're 1/6 your Earth weight.

• Mass (kg) ≠ Weight (N)
• Weight = mass × gravity
• 1 kgf = 9.81 N on Earth
• Weightless in orbit = still have mass

Contact forces touch objects (friction, tension). Non-contact forces act at distance (gravity, magnetism, electric).

• Tension pulls along ropes/cables
• Friction opposes motion
• Normal force perpendicular to surfaces
• Gravity always attractive, never repulsive

Newton (N) is the SI base unit. Defined from fundamental constants: kg, m, s. Used in all scientific work.

• 1 N = 1 kg·m/s² (exact)
• kN, MN for large forces
• mN, µN for precision work
• Universal in engineering/physics

Force units based on Earth's gravity. 1 kgf = force to hold 1 kg against gravity. Intuitive but location-dependent.

• kgf = kilogram-force = 9.81 N
• lbf = pound-force = 4.45 N
• tonf = ton-force (metric/short/long)
• Gravity varies ±0.5% on Earth

Dyne (CGS) for small forces: 1 dyn = 10⁻⁵ N. Poundal (imperial absolute) rarely used. Atomic/Planck forces for quantum scales.

• 1 dyne = 1 g·cm/s²
• Poundal = 1 lb·ft/s² (absolute)
• Atomic unit ≈ 8.2×10⁻⁸ N
• Planck force ≈ 1.2×10⁴⁴ N

1st: Objects resist change (inertia). 2nd: F=ma quantifies it. 3rd: Every action has equal opposite reaction.

• Law 1: No net force → no acceleration
• Law 2: F = ma (defines newton)
• Law 3: Action-reaction pairs
• Laws predict all classical motion

Forces combine as vectors, not simple sums. Two 10 N forces at 90° make 14.1 N (√200), not 20 N.

• Magnitude + direction required
• Use Pythagorean theorem for perpendicular
• Parallel forces add/subtract directly
• Equilibrium: net force = 0

Four fundamental forces govern universe: gravity, electromagnetism, strong nuclear, weak nuclear. Everything else is combinations.

• Gravity: weakest, infinite range
• Electromagnetic: charges, chemistry
• Strong: binds quarks in protons
• Weak: radioactive decay

Buildings withstand enormous forces: wind, earthquakes, loads. Columns, beams designed for kN to MN forces.

• Bridge cables: 100+ MN tension
• Building columns: 1-10 MN compression
• Wind on skyscraper: 50+ MN lateral
• Safety factor typically 2-3×

Rocket thrust measured in meganewtons. Aircraft engines produce kilonewtons. Every newton counts when escaping gravity.

• Saturn V: 35 MN thrust
• Boeing 747 engine: 280 kN each
• Falcon 9: 7.6 MN at liftoff
• ISS reboost: 0.3 kN (continuous)

Torque wrenches, hydraulics, fasteners all rated in force. Critical for safety and performance.

• Car lug nuts: 100-140 N·m torque
• Hydraulic press: 10+ MN capacity
• Bolt tension: kN range typical
• Spring constants in N/m or kN/m

Divide by 10 for estimate: 100 N ≈ 10 kgf (exact: 10.2)

• 1 kgf = 9.81 N (exact)
• 10 kgf ≈ 100 N
• 100 kgf ≈ 1 kN
• Quick: N ÷ 10 → kgf

1 lbf ≈ 4.5 N. Divide N by 4.5 to get lbf.

• 1 lbf = 4.448 N (exact)
• 100 N ≈ 22.5 lbf
• 1 kN ≈ 225 lbf
• Mental: N ÷ 4.5 → lbf

1 N = 100,000 dyne. Just move decimal 5 places.

• 1 dyn = 10⁻⁵ N
• 1 N = 10⁵ dyn
• CGS to SI: ×10⁻⁵
• Rarely used today

Saturn V rocket thrust: 35 MN. Convert to pound-force.

35 MN = 35,000,000 N. 1 N = 0.22481 lbf. 35M × 0.22481 = 7.87 million lbf

70 kg person. Weight on Earth vs Mars (g = 3.71 m/s²)?

Earth: 70 × 9.81 = 686 N. Mars: 70 × 3.71 = 260 N. Mass same, weight 38%.

Bridge cable supports 500 tons. What's the tension in MN?

500 metric tons = 500,000 kg. F = mg = 500,000 × 9.81 = 4.9 MN

Jaw's masseter muscle exerts 400 N bite force (900 lbf). Crocodile: 17 kN. Extinct Megalodon: 180 kN—enough to crush a car.

Flea jumps with 0.0002 N force but accelerates at 100g. Their legs are springs storing energy, releasing it faster than muscle can contract.

Near black hole, tidal force stretches you: feet feel 10⁹ N more than head. Called 'spaghettification.' You'd be ripped atom by atom.

Moon's gravity creates tides with 10¹⁶ N force on Earth's oceans. Earth pulls Moon back with 2×10²⁰ N—but Moon still escapes 3.8 cm/year.

Spider silk breaks at ~1 GPa stress. Thread with 1 mm² cross-section would hold 100 kg (980 N)—stronger than steel by weight.

AFM feels forces down to 0.1 nanonewton (10⁻¹⁰ N). Can detect single atom bumps. Like feeling a grain of sand from orbit.

Newton publishes Principia Mathematica, defining force with F = ma and three laws of motion.

Pierre Bouguer measures gravitational force on mountains, notices variations in Earth's gravity field.

Cavendish weighs Earth using torsion balance, measuring gravitational force between masses.

British Association defines 'dyne' (CGS unit) as 1 g·cm/s². Later, newton adopted for SI.

CGPM defines newton as kg·m/s² for SI system. Replaces old kgf and technical units.

SI officially adopted globally. Newton becomes universal force unit for science and engineering.

Atomic force microscope invented, detecting piconewton forces. Revolutionizes nanotechnology.

SI redefinition: newton now derived from Planck constant. Fundamentally exact, no physical artifact.

Mass (kg) is the amount of matter; weight (N) is gravitational force on that mass. Mass stays constant; weight changes with gravity. You weigh 1/6 on Moon but have same mass.

Newton is absolute—doesn't depend on gravity. kgf/lbf assume Earth's gravity (9.81 m/s²). On Moon or Mars, kgf/lbf would be wrong. Newton works everywhere in the universe.

Average person: 400 N push, 500 N pull (short burst). Trained athletes: 1000+ N. World-class deadlift: ~5000 N (~500 kg × 9.81). Bite force: 400 N average, 900 N max.

Kip = 1000 lbf (kilopound-force). US structural engineers use kips for bridge/building loads to avoid writing big numbers. 50 kips = 50,000 lbf = 222 kN.

Rarely. Dyne (CGS unit) appears in old textbooks. Modern science uses millinewtons (mN). 1 mN = 100 dyn. CGS system is obsolete except in some specialized fields.

Weight IS force. Formula: F = mg. Example: 70 kg person → 70 × 9.81 = 686 N on Earth. On Moon: 70 × 1.62 = 113 N. Mass (70 kg) doesn't change.