The Forge of Force

NODE 01

The Idea of Force

• Push/pull as an interaction.
• Force as a vector (Magnitude + Direction).
• Kinematics = what. Dynamics = why.

NODE 02

Interactions

• Contact forces: Normal, Friction, Tension, Spring.
• Field forces: Gravitational, Electric, Magnetic.

NODE 03

Fundamental Forces

• Gravitational, Electromagnetic.
• Strong nuclear, Weak nuclear.
• All ordinary forces connect to these.

NODE 04

Newton's First Law

• Law of Inertia.
• Objects remain at rest or uniform motion...
• ...unless acted upon by a net external force.

NODE 05

Inertia

• Resistance to change in motion.
• Rest, motion, and direction.
• Mass is the measure of inertia.

NODE 06

Newton's Second Law

F = ma

• Net force → change in momentum.
• Acceleration follows the net force.
• F = ma (for constant mass).

NODE 07

Newton's Third Law

• For every interaction: forces occur in pairs.
• Equal magnitude, opposite direction.
• Act on DIFFERENT objects (they do not cancel).

NODE 08

Free-Body Diagrams

• Isolate object, identify all forces.
• Draw vectors, choose axes, resolve components.
• The universal language of mechanics.

NODE 09

Weight & Mass

MASS (kg)vsWEIGHT (N)

• Mass: Inertial property (constant).
• Weight: Gravitational force (W = mg).
• Changes with local gravity.

NODE 10

Normal Reaction

• Surface contact, perpendicular force.
• Not automatically equal to mg!
• Apparent weight in elevators/inclines.

NODE 11

Tension

• String/rope force, pulls along the string.
• Ideal string/pulley approximations.
• Connected-body systems.

NODE 12

Friction

• Resisting interaction between surfaces.
• Static (prevents slipping) up to f_max = μ_s N.
• Kinetic (during motion) f_k = μ_k N.

NODE 13

Useful Friction

• Friction allows walking, driving, gripping.
• It is not simply "bad".

NODE 14

Drag

• Air/water resistance.
• Depends on speed and shape.
• Leads to Terminal speed.

NODE 15

Equilibrium

• Force balance: ΣF = 0.
• Static (at rest) or Dynamic (constant velocity).
• Net force zero ≠ object is at rest.

NODE 16

Inclined Planes

• Resolve weight: mg sinθ (parallel).
• mg cosθ (perpendicular).
• Combines vector math with dynamics.

NODE 17

Momentum

p = mv

• Measures the "motion-content" of a body.
• Vector quantity. Central to collisions.

NODE 18

Impulse

• Connects force and momentum: J = FΔt = Δp.
• Large force/short time vs Small force/long time.
• Airbags, helmets, catching.

NODE 19

Cons of Momentum

• For an isolated/closed system.
• Total momentum before = Total momentum after.
• Internal forces cancel out.

NODE 20

Collisions

💥

• Elastic: Momentum & Kinetic Energy conserved.
• Inelastic: Momentum conserved, KE not.
• Perfectly inelastic: Objects stick together.

NODE 21

Center of Mass

• Average position weighted by mass.
• Motion of a system as a single point.
• Internal vs external forces.

NODE 22

Rockets (Preview)

• Variable mass system.
• Gas expelled backward → Rocket moves forward.
• Momentum conservation & Thrust.

NODE 23

Circular Dynamic

• Fc = mv²/r = mω²r.
• Centripetal force is NOT a new mysterious force.
• It is the NET inward force required.

NODE 24

Non-Inertial Frames

• Accelerating reference frames (Lifts, turning cars).
• Apparent/Pseudo forces arise.

NODE 25

Force Systems

• Collinear, Concurrent, Parallel.
• Coplanar, Distributed forces.
• Expands beyond simple one-object problems.

NODE 26

Resultant Force

• Combining multiple forces (ΣF) via vector methods.
• Connects Realm 03 to acceleration.

NODE 27

F-a Graphs

• Experimental relationships.
• F ∝ a (constant mass). F ∝ m (fixed accel).
• Newton's 2nd Law as measurable data.

NODE 28

Experimental Forge

m

F

μ

a

• Verify inertia, measure friction.
• Momentum-cart collisions, impulse data.
• Apparatus → Obs → Graph → Calc.

NODE 29

Solving Engine

• READ → DRAW → ISOLATE → FBD → AXES.
• RESOLVE → ΣF = ma → CONSTRAINTS → SOLVE.
• Must become automatic.

NODE 30

Exit Gate

• Force explains changes in motion.
• But what happens when force acts through distance?
• Opens REALM 05: The Wheel of Motion.