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Physics I   De-Briefing

What you really should have learned in Physics 1

Foundation #1 : distinguish each item from its properties (quantities)
      and its internal properties from its contributions to the environment
. . . one item's properties might change ("Δ") as time passes, even tho' it is the same item later
      intrinsic properties (mass) do not change (since it contains the same molecules)
. . . this is distinct from some property being different (having a different value)
      at a different place ("δ"), or for some different item
      hint: identify different items for yourself by meaningful number or letter subscripts !
. . . Physics equations are always only about properties − never about items
      it is the properties that you will be asked to compare (or find the difference of)

Foundation #3 : organize givens and sought-afters on a diagram
      a thing's behavior depends on its environment, whose Nature is sustained by where things are (relative to it).
. . . choose a perspective so uncancelled Forces show flat on the page - coordinates along (and  |  to) acceleration   (or v)
      equations relate system-bag interior (behavior change) with influences that pierce the bag (cross the system boundary)
      ... the desired unknown must be one of these, to show up so it can be solved for!
. . . one situation diagram for conditions at one instant (snapshot, not process)
      situation questions relate Force or Field components with acceleration, or continuous flow geometries
. . . one "before-to-after" scenario if a process moves a thing to a different place in constant landscape
      usually best to treat a "where" question using Energy & Work approach
. . . two diagrams - "before" and "after" - if a process changes the thing or landscape time-wise (not place)
      usually best to treat a "when" question using momentum & Force approach.

Foundation #4 : reason via concepts ... passive object properties are changed by active subjects
      use cause-to-effect or story-line order ... translate words to symbols ... solve for needed variable
. . . practice subject-predicate-object ... using correct prepositions! ... learn cause-to-effect factors - with mitigations
      (don't try to memorize an equation for every question ... or for every situation)
. . . Physics textbooks write every relationship as an "equals" ... very few are
      "=" is symmetric, but causal relations are anti-symmetric!
      it is the multiple causes (contributions) that get added (perhaps to cancel)
. . . Natural cause-to-effect order: subject(s) do a (relational) predicate to an object
      a) each subject "tries to" do something ... they each make a contribution ... add these !
      ... use subscript modifiers to distinguish which subject makes this contribution
      b) the object gets something done to it ... 1 object, it can only respond 1 way ...
      ... when 2 things interact, you get to choose (perspective) which is subject and which is object

Foundation #5 : physically-important quantities are related to several others
      so their variable symbols show up in several distinct equations
a) where does it come from / how does Nature produce it / what is its source / theory
      how does the subject item (present tense) modify its environment
      subject formula examples: Lunar gravity, spring Force, Kinetic Energy ...
. . . proximity to Moon (−GM/r² => g_moon ) , a stiff spring stretched (−ks) , accumulated motion (½p·v)
b) what does it do / what influence does it promote / / how can we measure its value / what does it make happen / experiment
      how is the environment influencing the object item (of interest) ; hammer's mass in gravity (mg_moon)
. . . predicate object (ex: ΣF   causes mass to accelerate, or momentum change over time change ... )
. . . factors in a formula describe either a) subject with relevent conditions ; or b) object in its environment
c) how does it change / what else happens when it changes / what if it is different close-by / feedbacks & patterns
      a conserved scalar (inside) can only change as its vector current flows (in or out)
      an Energy difference nearby implies that a Force is exerted along (or against) that path
      curvature of Potential Energy shows up in oscillations & waves

Foundation #6 : many quantities are directional vectors , but not all of them
. . . vector B adds to vector A by placing B's tail at A's tip (both oriented as before)
      the sum C is a vector from first tail pointing straight to last tip ... but only if they have same units!
      ( B's difference from A: with tails together, arrow from A's tip to B's tip
. . . a scalar times a vector   ( F Δt ) is like repeated vector addition
      yields a vector along (pointed in the same direction as) the original ... opposite, if negative scalar
. . . one vector pointing along another vector   ( F · Δx ) multiplies their parallel portion
      the "dot product" yields a scalar (negative, if the 2 vectors oppose)
. . . one vector pointing across another vector ( r × F ) multiplies in 3-d, finding the portion around the first's tail (  |  )
      the "cross product" vector direction points in via right-hand-rule (Thumb, if wRist × Fingers)

Foundation #7 : story-line (time) order: starting condition , is changed by processs , into ending status
      intro + plot happens => end ... conditions might change during a process
. . . "initial" condition assigns momentums, Eneries, locations, etc. as the process starts being watched
      process endures for a time duration (Δt) while displacements (Δx) and other changes accumulate
      "final instant" conditions, after the process has endured a while, are usually different than they used to be.
. . . "boost" example:   v_before + Δv = v_after   ... boost   Δv = aΔt   is a process since it's proportional to Δt
. . . "Work":   KE_i + PE_grav,i + PE_spr,i + Work_{no_PE_form} = KE_f + PE_grav,f + PE_spr,f ... Work is a process since it's done during Δt
      Impulse (J) and Work (W) and Heating Quantity (Q) are processes, even though their symbols lack a Δ
      ... J = F Δt ... W = F·Δx ... Q = Δt ... ( is Power) ... what quantity does each effect?
. . . a product being accumulated is always   (average condition) (total change)   during the accumulation
      "Work" example:   W = F·Δx = F_avg·Δx_tot   => ("causes") v_avg · Δp_tot

Foundation #8 : in real life, stuff is spread out !
. . . conserved item scalars are spread over the item's Volume , becoming densities ( ρ_E = E / Vol )
      the scalar quantity is inside the item's surface Area ... (a closed boundary)
=> scalar Quantity "aggregated" inside = (average density) (total Volume)
. . . vector quantities are spread transverse to their direction arrow, over a 2-d cross-section Area
      the vector quantity pierces thru the cross-section surface along the Area vector
      Area is a vector (L × W ) that is Normal (perp.) to the surface
=> vector quantity aggregated thru the Area = (average vector field intensity) · (total Area)
. . . "pressure" example:   PA = F_N
.