OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Direction Cosine Matrix to Euler 232 Sequence

Starting with a direction cosine matrix (DCM), we need to determine the three Euler angles. The connection is made by comparing the DCM elements with the combined Euler 232 sequence. It is important to note that the 12 combinations of Euler angles for a given sequence can be found from a given DCM. The DCM matrix is
   $DCM=\left[{\begin{matrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{matrix}}\right]$
The Euler 232 sequence is
   $R_{2}(\psi )R_{3}(\theta )R_{2}(\phi )=\left[{\begin{matrix}c_{\psi }c_{\theta }c_{\phi }-s_{\psi }s_{\phi }&c_{\psi }s_{\theta }&-c_{\psi }c_{\theta }s_{\phi }-s_{\psi }c_{\phi }\\-s_{\theta }c_{\phi }&c_{\theta }&s_{\theta }s_{\phi }\\s_{\psi }c_{\theta }c_{\phi }+c_{\psi }s_{\phi }&s_{\psi }s_{\theta }&-s_{\psi }c_{\theta }s_{\phi }+c_{\psi }c_{\phi }\end{matrix}}\right]$
If we examine the element in coloum 2 row 2, then by inspection
$A_{22}=cos(\theta )$
Solving for $\theta$ yields
   $\theta =cos^{-1}(A_{22})$
Care must now be taken when evaluating the inverse cosine. It is a multivalued function. Analytically, the convention is to choose the principle value such that
$0\leq \theta \leq \pi$
If a numerical program is used, a function acos usually does this for us. The next step is to analyze the ratio ${\frac {A_{23}}{A_{21}}}$. Using these values from the Euler sequence we get
${\frac {A_{23}}{A_{21}}}={\frac {sin(\theta )sin(\phi )}{-sin(\theta )cos(\phi )}}$
Rearranging and using the tangent yields
$tan(\phi )={\frac {A_{23}}{-A_{21}}}$
Solving the quadrant ambiquity caused by the inverse tangent is done by examining the signs of the numerator and denominator. Denoting y as the numerator and x as the denominator, then the quadrant is chosen by:
quadrant 1 </math> \left[ \begin{matrix} y & x \\ + & + \\ \end{matrix} \right] $soifxandyarebothpositive,then<math>0\leq \phi \leq \pi /2$. Similarily for the other quadrant possibilites
quadrant 2 </math> \left[ \begin{matrix} y & x \\ + & - \\ \end{matrix} \right] $quadrant3$ \left[ \begin{matrix} y & x \\ - & - \\ \end{matrix} \right] $quadrant4$ \left[ \begin{matrix} y & x \\ - & + \\ \end{matrix} \right] $Ofcourse,itismuchsimpliertouseacalculatorornumericalprogramthatusestheatan2functionwhichwillchoosetheprinciplevalue.InasimilarfashionwecanfindthefinalEuleranglebylookingattheratio<math>{\frac {A_{32}}{A_{12}}}$ which gives the relation ${\frac {A_{32}}{A_{12}}}={\frac {sin(\psi )sin(\theta )}{cos(\psi )sin(\theta )}}$
Canceling terms and rearrangeing gives us
$\psi =tan^{-1}({\frac {A_{32}}{A_{12}}})$
which uses the same method to resolove quadrant ambiguity as above. To summarize, we will give the formulas for the conversion from a direction cosine matrix to the Euler 232 angles in Matlab syntax. Be careful how you implement this in other numerical programs. In Matlab it goes atan2(y,x) and in Mathematica it is ArcTan[x, y].
$\phi =atan2(A_{23},-A_{21})$ $\theta =acos(A_{22})$ $\psi =atan2(A_{32},A_{12})$
# PlanetPhysics/Direction Cosine Matrix to Euler 313 Angles

Starting with a direction cosine matrix (DCM), we need to determine the three Euler angles. The connection is made by comparing the DCM elements with the combined Euler 313 sequence. It is important to note that the 12 combinations of Euler angles for a given sequence can be found from a given DCM. The DCM matrix is
   $DCM=\left[{\begin{matrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{matrix}}\right]$
The Euler 313 sequence is
   $R_{3}(\psi )R_{1}(\theta )R_{3}(\phi )=\left[{\begin{matrix}c_{\psi }c_{\phi }-s_{\psi }s_{\phi }c_{\theta }&c_{\psi }s_{\phi }+s_{\psi }c_{\theta }c_{\phi }&s_{\psi }s_{\theta }\\-s_{\psi }c_{\phi }-c_{\psi }s_{\phi }c_{\theta }&-s_{\psi }s_{\phi }+c_{\psi }c_{\theta }c_{\phi }&c_{\psi }s_{\theta }\\s_{\theta }s_{\phi }&-s_{\theta }c_{\phi }&c_{\theta }\end{matrix}}\right]$
If we examine the element in coloum 3 row 3, then by inspection
$A_{33}=cos(\theta )$
Solving for $\theta$ yields
   $\theta =cos^{-1}(A_{33})$
Care must now be taken when evaluating the inverse cosine. It is a multivalued function. Analytically, the convention is to choose the principle value such that
$0\leq \theta \leq \pi$
If a numerical program is used, a function acos usually does this for us. The next step is to analyze the ratio ${\frac {A_{31}}{A_{32}}}$. Using these values from the Euler sequence we get
${\frac {A_{31}}{A_{32}}}={\frac {sin(\theta )sin(\phi )}{-sin(\theta )cos(\phi )}}$
Rearranging and using the tangent yields
$tan(\phi )={\frac {A_{31}}{-A_{32}}}$
Solving the quadrant ambiguity caused by the inverse tangent is done by examining the signs of the numerator and denominator. Denoting y as the numerator and x as the denominator, then the quadrant is chosen by:
quadrant 1 $\left[{\begin{matrix}y&x\\+&+\\\end{matrix}}\right]$
so if x and y are both positive, then $0\leq \phi \leq \pi /2$. Similarly for the other quadrant possibilities
quadrant 2 $\left[{\begin{matrix}y&x\\+&-\\\end{matrix}}\right]$
quadrant 3 $\left[{\begin{matrix}y&x\\-&-\\\end{matrix}}\right]$
quadrant 4 $\left[{\begin{matrix}y&x\\-&+\\\end{matrix}}\right]$
Of course, it is much simplier to use a calculator or numerical program that uses the atan2 function which will choose the principle value. In a similar fashion we can find the final Euler angle by looking at the ratio ${\frac {A_{13}}{A_{23}}}$ which gives the relation ${\frac {A_{13}}{A_{23}}}={\frac {sin(\psi )sin(\theta )}{cos(\psi )sin(\theta )}}$
Canceling terms and rearrangeing gives us
$\psi =tan^{-1}({\frac {A_{13}}{A_{23}}})$
which uses the same method to resolove quadrant ambiguity as above. To summarize, we will give the formulas for the conversion from a direction cosine matrix to the Euler 313 angles in Matlab syntax. Be careful how you implement this in other numerical programs. In Matlab it goes atan2(y,x) and in Mathematica it is ArcTan[x, y].
$\phi =atan2(A_{31},-A_{32})$ $\theta =acos(A_{33})$ $\psi =atan2(A_{13},A_{23})$
# Informal learning activities/Atl

Astrl
This inserts a link to the country or area, in this case Australia, into a Places & Buildings item.
# Informal learning activities/BBwC

Beings & Behaviourː C__  O ther initialsː   Ab
(«»C⇓⇓)
 Df
 Gi  Jl
 Mo  Pr
 Su  Vz
• cabal (plot)
 cachalot (whale)
 cade (juniper)
 cadi (judge)
 caique (parrot)
 calcar (bat spur)
 cambist (banker)
 campion (plants)
 caique (parrot)
 calcar (bat spur)
 camash (asparagus⊂)
 cambist (banker)
 camogie (hurling4w )
 campion (plants)
 cancroid (crabby+)
 canna (~lily)
 canthi/us (<eye>)
 cantle (saddle⊂)
 capon (castrato)
 capot (piquet⊂)
 caprid/ne (bovid + )
 carcajou (wolverine) carex (sedge)
 caribou (≈reindeer)
 caries (decay)
 cark (worry)
 carny (@ –ival)
 carpel (pistil⊂)
 carr (fen)
 caulis (stalk)
 cautery (sear)
 cavil (carp)
 cavort (caper)
 cavy (rodent)
 cayuse (horse)
• caecum (gut⊂)
 ceiba (tree)
 cellule (cell )
 cercal/i/us (tail)
 ceriman (epiphyte)
 cero (fish) certes (truly)
 cervine (deerish)
 cession (ceding)
 cete (badgers)
• chalone (hormone)
 chancre (sore)
 chantry (mass)
 chee/ital (deer)
 chela (claw)
 chevrotain (deer )
 chirm (din)
 chiton (mollusc)
 choko (gourd)
 cholic (pain)
 cholla (cacti+)
 chorea (disorder)
 chough (crow)
• cibolero (hunter)
 cilium/a (organelle)
 cimex (bed bug)
 cinch (doddle)
 cisco (fish) civet (night cat)
• clachan (village)
 clade (group)
 claque (sycophants)
 clary (sage)
 clavate (clubbish)
 clave (rhythm) clef (pitch)
 cleg (fly)
 clench (grip)
 cline (gradation)
 clonic/us (twitch)
• cnemis (⊂shin)
• coakum (pokeweed)
 coati (raccoon)
 coda (tail)
 codon (gene⊂)
 coeliac (disease)
 coelom (gut⊂)
 coffle (chain)
 coho (salmon)
 cola (drink)
 cole (plant)
 colic (pain)
 collie (dog)
 coly (bird)
 comber (fish) comity (reciprocity)
 conch (c snail)
 concha (ear⊂)
 condor (vulture)
 congener (relative)
 conger (eel)
 conium (⊂hemlock)
 conk (hair⊂)
 conker (tree)
 conure (parrot)
 conus (c snail)
 coney (rabbit)
 coonti (cycad)
 coracoid (shoulder⊂)
 cordon (canopy⊂)
 corella (bird) corium (dermis) corneous (horny)
 correa (plant) corvine/us (crowy)
 coryza (cold)
 costa (rib)
 cova/en (witches)
 cowhage (vine)
 cowan (~mason)
 cower (cringe)
 cowitch (vine)
 cowrie/y (c snail)
 coxa (hip) coypu (rodent)
 cozener (swindler)
• cracid (bird)
 crake (rail!)
 crambo (rhyme)
 crenate (scalloped)
 craw (crop) cretic (poetry)
 cría (alpaca)
 croton (plant) croup (≈cough)
 crowea (shrub)
 crus (leg+)
• culm (stem)
 cummin (plant)
 curia (council)
 curli (fibril)
 curvet (leap)
 cuscus (possum)
 cutin (∊cuticle)
 cutis (∊skin+)
• cycad (plant)
 cyclops (water flea)
 cyclosis (cell⊂flow)
 cyme (flower)
# Informal learning activities/BBwDf

Beings & Behaviourː D⇒ F__  O ther initialsː   Ac
(«»Df⇓⇓)
 Gi  Jl
 Mo  Pr
 Su  Vz
• dactyl (poetry) dahu (beast)
 dhal (lentils)
 daikon (radish)
 danio (fish )
 dassie (hyrax)
• dementia (madden)
 demy (student)
 dens (axis⊂)
 dentin (tooth⊂)
 descant (song)
 destrier (warhorse)
 deus (god)
 dewan (ruler)
• dilsk (alga )
 dingus (dolt)
 discant (song)
 diwan (title)
• doat (dote)
 dodder (plant)
 doge (chief)
 dorcas (gazelle )
 douc (monkey)
 douceur (bribe+)
 dour (sullen)
 dower (widowage)
 dowitcher (wader)
 dowser (divine+ )
• driver (ant)
 drongo (bird)
 dropsy (swelling)
 drupe (fruit)
• duiker (antelope )
 dulia (veneration) duls/ce (alga )
 durra (sorghum)
 duramen (heartwood)
 durmast (oak)
Beings & Behaviourː E__
{../STc|merocrine|eccrine|sweaty}} ecesis (establishment)
 éclat (wow!)
 eclose (emerge)
• educe (elicit)
 egest (excrete )
 egga/er (moth)
• eider (duck)
 élan (go)
 elemi (tree)
• emesis (vomiting) emmet (ant)
• endonym ([name])
 enfeoff (give)
 ennui (boredom) • eparch (ruler)
 equinia (disease)
 ergot (fungus)
 eristic (argument)
 erne (sea eagle)
 eros (libido )
 erose (jagged)
 eruct (belch)
 erva (herb)
• eschar (~scab)
 escheat (property⇒)
 escrow (entrust)
 esparto (grass)
 essive (case)
• euphuism (prose!)
 exine (pollen⊂)
 exon (gene⊂)
 exonym name
 eyra (cat )
 eyre (circuit)
Beings & Behaviourː F__
• falcula (claw)
 farcy (disease)
 faro (game)
 fauces (throat⊂)
• feoffee (trustee)
 femur (bone)
 feria (holiday)
 fetial (priest)
• fiat (decree)
 fibula (bone)
 fieldfare (thrush)
 filbert (hazel)
 filch (nick)
 finfoot (bird)
 firman (decree)
 fitch (polecat)
• flatus (fart)
 floret (flower )
• forb (flower)
 formant (⊂resonance)
 forte (loud )
 fortis (tense)
 fossa (civet)
 fovea (retina⊂)
• frog (hoof⊂) frons (forehead)
• fundus (bottom)
 furca (insect⊂)
 fuscous (dark )
 fusilier (soldier)
 futsal (soccer )
# Informal learning activities/BBwGi

Beings & Behaviourː G⇒ I__  O ther initialsː   Ac  Df
(«»Gi⇓⇓)
 Jl
 Mo  Pr
 Su  Vz
• galea (cavy) gall (blister)
 galop (dance)
 gamete (cell)
 gamine (f urchin)
 garget (pokeweed)
 garron (pony)
 gaur (bison)
 gayal (bison)
 gavial (croc)
• gemma (fragment) genet (~cat)
 genic (geney)
 genie (jinn) genista (legume)
 genitor (parent)
 gens (family)
 genu (knee)
 german (dance)
 gerenuk (gazelle)
 geum (herb)
• giaour (heathen)
 gigue (dance)
 gila (animals)
 giro (payment)
• glans (genital)
 glenoid (bon e)
 glia (cells)
 glire (rodent)
• goiter/re (lump)
 golem (monster)
 gomuti (palm)
 gopak (dance)
 goral (antelope)
• greffier (notary)
 grilse (fish)
 grivet (monkey)
 grue (shudder)
 grump (groucher)
• guan (bird) guano (poop)
 guar (bean)
• gurn (grimace)
 gurnard (fish)
 gyascutus (beast )
Beings & Behaviourː H__
• haptic (touchy)
 harry (harass)
 hart (deer) hartal (strike)
• helot (serf)
 hepatic (re liver)
 herl (barb+)
• hie (hurry)
 hilum (fissure)
 hispid (hairy+ )
• hoopoe (bird)
 hopak (dance)
 hoplite (soldier)
 hora (o dance)
 hosta (~lily)
 houri (lass)
 howitzer (gun)
• huia (wattlebird)
 hula (dance)
Beings & Behaviourː I__
• ichor (bile) ictus (stroke)
 ileus (disorder)
 ilium (bone) •
 impi (regiment)
• incross (inbred )
 incus (ear⊂)
 inion (skull⊂)
 inker (artist)
 intima (≈undercoat)
 intine (pollen⊂)
 introit (liturgy)
• iter (circuit)  •
 ixia (plant)
# Informal learning activities/BBwJl

Beings & Behaviourː J⇒ L__  O ther initialsː   Ac
 Df  Gi
(«»Jl⇓⇓)
 Mo  Pr
 Su  Vz
• jabot (craw+) jacana (wader)
 jacquerie (revolt)
• jejune (dull+)
 jejunum (∈gut)
 jerboa (rodent)
• jink (dodge+)
 jinn (genies )
 jurat (judge)
 jussive (mood)
Beings & Behaviourː K__
• kaka (parrot)
 karo (tree)
 katydid (cricket)
• kendo (fencing)
 keno (gamble)
 kentia (palm)
 kermes (insect) • kina (sea urchin) kinase (enzyme)
 kip (hide + )
• koel (cuckoo)
 koonti (cycad)
 kopi (tree)
Beings & Behaviourː L__
• labret (lip hole)
 laic (layperson) lamia (rodent)
 lamium (~nettle)
 lamprey (~eel)
 larva (infant)
 latria (adoration)
 laver (seaweed) lazzaroni (mob )
• lector (reader)
 legist (lawyer)
 legume (plant)
 leman (mistress+ )
 lenis (lax)
 lento (slow+ )
 lerp (>insect<)
 lethe (oblivion)
 levigate (smooth+ )
• libero (soccer⊂) lictor (bodyguard)
 liger (~tigon)
 lima (clam)
 limbus (corneal)
 limn (illuminate)
 ling (heather)
 linnet (finch)
 litotes (rhetoric)
• lobo (wolf)
 lobule (lobe )
 lochia (discharge)
 locule (cavity )
 logion (saying)
 logos (persuasion)
 loment (legume)
 lory (parrot)
 lote (tree)
 lotic (flowing)
• luce (pike )
 lucerne (pea)
 luffa (vine)
 lumen (cavity)
 luna (moth)
 lustration (cleaning)
 lunula (∈nail)
 lupus (disease)
 lurgi (illness)
 luth (turtle)
• lysis (cell⇓)
 lyssa (rabies )
# Informal learning activities/BBwAb

Beings & Behaviourː A B__  O ther initialsː  («»Ab⇓⇓)
 C  Df
 Gi  Jl
 Mo  Pr
 Su  Vz
• abator (law)
 abele (poplar)
 ablate (erode)
 ablative (case)
• acaridae (mite)
 acer (maple)
 acerate/ose (needly)
 ach/kene (fruit)
 acinus (drupe+ )
• adage (saying)
 addax (≈oryx )
 adnate (joined)
 aegis (shield)
 aero (flight)
• agave (succulent)
 agio (premium)
 agley (awry)
 agnate/ic/ion (patrilineality )
 agouti (rodent)
 alalia (mutism)
 alap (music)
 alar (chemical)
 alate (insect⊂)
 albugo (rust)
 alburnum (sapwood)
 alcai/yde (leader)
 alerce (cypress)
 alevin (fish )
 alfalfa (pea)
 algid (cold )
 allium (garlic+)
 aloe (plant)
 alula (wing )
 alvine (gutsy )
• ambari/y (kenaf )
 amee/ir (emir)
 ammi (wort)
 ammine (–ammonia)
 amnio (diagnosis)
• ananas (⊂pineapple)
 ancle (c→k)
 ancon (bracket+)
 angst (fear)
 animus (dislike+ )
 anoa (buffalo )
 anole (lizard)
 anomie/y (asocial)
 anuria (p̶i̶s̶s̶)
• aorta (artery)
 apery (mimicry)
 aphis (insects)
 apian (bees)
 apical (tip)
 apnoea (b̶r̶e̶a̶t̶h̶)
 appel (footwork)
• arachis (pea)
 arco (→bowed)
 areal (adj.! )
 arene (hydrocarbon)
 areola (°skin)
 virtue (arete) argal (so)
 argali (sheep)
 argot (≈slang)
 argus (pheasant)
 ariel (gazelle )
 aril ([seed])
 arnica (sunflower)
 aroid (arum)
 aroint (go!)
 arpent (unit )
 arsis (music⊂)
 arum (plant)
 aryl (chemical)
• ascites/ic (belly)
 ascus/i (fungus⊂)
 aster (flower)
 astilbe (saxifrage)
• ataman (leader)
 atlas (spine⊂)
 atman (soul)
 atonic/y (muscle)
 atrium (chamber)
 attap (palm)
 attar (fragrance)
 attorn (re tenancy)
• augur (priest)
 aula (hall)
 aurist (audiologist )
 auricle (ear⊂)
• axel (skating)
 axillary (armpit)
 axis (spineC2 )
 azygos (asymmetrical)
Beings & Behaviourː B__
• bael (tree)
 baillie (magistate)
 balatá (tree)
 baleen (filter)
 balsa (tree)
 balut (game)
 banal (blah)
 banc (court)
 banco (mudbrick)
 bandanna (kerchief)
 banket (pastry)
 bant (diet)
 bantam (poultry)
 banteng (cattle)
 baobab (tree)
 baron (butterfly)
 barouche (carriage)
 barria (fungi)
 basion (forehead)
 basso (voice)
 bhatta (>pay+)
 battue (hunt)
• benne (sesame) be/i/urk (twit)
 betony (plant)
• bile (gall)
 bilk (cheat)
 binal (double)
 bine (climber)
 bint (girl)
 biome (ecosystem)
 biota (cypress)
 bisque (soup)
 bittern (heron)
• blag (rob)
 blain (distemper)
 blenny (fish)
 blet (fruit rot)
 bloat (inflation)
• boab (tree)
 bohunk (insult)
 bolus (dose+)
 bonce (head)
 bonito (tuna)
 bonsai (tree)
 bonze (monk)
 bott (fly)
 bouvier (grape)
 bolyar (prince)
• bract (leaf)
 brant (goose)
 bregma (skull⊂)
 breech (bum)
 brill (fish) brio (vigour+ )
 brit (fish )
 brome (grass)
 broom (plant)
 brogue (accent)
 bruit (sound)
• bubo (blister+ )
 bufo (toad)
 bulbul (songbird)
 buna (beech)
 bunya (pine)
 burgess (title) burley (bait)
 bursa (sac)
 burse (case+ )
 buss (kiss)
 butt (ram+ )
• bwana (sir)
 byssus (sea silk)
# Informal learning activities/BBwB

Beings & Behaviour: B__ Other initials: A stB C Df • bael (tree)
 baillie (magistate)
 balatá (tree)
 baleen (filter)
 balsa (tree)
 balut (game)
 banal (blah)
 banc (court)
 banco (mudbrick)
 bandanna (kerchief)
 banket (pastry)
 bant (diet)
 bantam (poultry)
 banteng (cattle)
 baobab (tree)
 barouche (carriage)
 barria (fungi)
 basion (forehead)
 basso (voice)
 bhatta (>pay+)
 battue (hunt)
• benne (sesame) be/i/urk (twit)
 betony (plant)
• bile (gall)
 bilk (cheat)
 binal (double)
 bine (climber)
 bint (girl)
 biome (ecosystem)
 biota (cypress)
 bisque (soup)
 bittern (heron)
• blag (rob)
 blain (distemper)
 blenny (fish)
 blet (fruit rot)
 bloat (inflation)
• boab (tree)
 bohunk (insult)
 bolus (dose+)
 bonce (head)
 bonito (tuna)
 bonsai (tree)
 bonze (monk)
 bott (fly)
 bouvier (grape)
 bolyar (prince)
• bract (leaf)
 brant (goose)
 bregma (skull⊂)
 breech (bum)
 brill (fish) brio (vigour+)
 brit (fish)
 brome (grass)
 broom (plant)
 brogue (accent)
 bruit (sound)
• bubo (blister+)
 bufo (toad)
 bulbul (songbird)
 buna (beech)
 bunya (pine)
 burgess (title) burley (bait)
 bursa (sac)
 burse (case+)
 buss (kiss)
 butt (ram+)
• bwana (sir)
• byssus (sea silk)
# Informal learning activities/BBwA

Beings & Behaviour: A__ Other initials: stA B C Df • abator (law)
 abele (poplar)
 ablate (erode)
 ablative (case)
/ • acaridae (mite)
 acer (maple)
 acerate/ose (needly)
 ach/kene (fruit)
 acinus (drupe+)
• adage (saying)
 addax (≈oryx)
 adnate (joined)
• aecium (fungus)
 aegis (protection)
 aery (lofty)
 aero (flight)
• agave (succulent)
 agio (allowance)
 agley (awry)
 agnate/ic/ion (patrilineal)
 agouti (rodent)
• alalia (mutism)
 alap (music)
 alary (winged)
 alate (insect+)
 albugo (rust)
 alcai/yde (leader)
 alerce (cypress)
 alevin (fish)
 alfalfa (pea)
 algid (cold)
 algor (chill)
 allium (onion)
 aloe (plant)
 alula (wing)
• ambari/y (kenaf)
 amee/ir (emir)
 ammi (wort)
 ammine (–ammonia)
 amnio (diagnosis+)
• angst (fear)
 ancle (c→k)
 ancon (bracket+)
 animus (dislike+)
 anoa (buffalo)
 anole (lizard)
 anomie/y (asocial)
 anuria (p̶i̶s̶s̶)
• aorta (artery)
• apery (mimicry)
 aphis (insect)
 aphotic (dark)
 apian (bees)
 apical (tip)
 apnoea (b̶r̶e̶a̶t̶h̶)
 appel (footwork)
• arco (bowed)
 areal (adj.!)
 arene (aromatic)
 areola (skin)
 arete (virtue)
 argal (so)
 argali (sheep)
 argot (slang)
 argus (pheasant+)
 ariel (gazelle)
 aril (seedish)
 arnica (bane)
 aroid (arum)
 aroint (go!)
 arsis (poetry)
 arum (plant)
 aryl (chemical)
• ascites/ic (beer belly)
 ascus/i (fungus)
 assai (palm+)
 aster (flower+)
 astilbe (saxifrage)
• ataman (leader)
 atlas (⊂spineC1+)
 atman (soul)
 atonic/y (muscle)
 atrium (chamber)
 attap (palm)
 attar (fragrance)
 attorn (tenancy+)
• augur (portend+)
 aula (⊂brain)
 aurist (audiologist)
 pinna (auricle)
• axel (skating)
 axillary (armpit)
 axis (spineC2+)
# Physics equations/Labs
## Static torque circle

* Record all results is a clear and concise manner.
* You may use "gm" as a unit of force (no need to multiply everything by g).
* Show your work using the language of vector algebra with components. "F" (with subscripts) is a nice symbol to use for your vectors.
* Use a calculator to perform your calculations.
* Also, enter your raw data into the spreadsheet at the front computer. (Just enter numbers, we will analyze them later).
* Set the table up so that zero degrees is aligned with the x axis. Mark that line with a ruler or other image of a ray.
* Calibrate your accuracy by arranging four equal and opposite tensions that aligned with the plus/minus x and y axes. Perform this calibration (with four forces at 90 degrees) five times, using different angles and weights.
* Set up three forces, using your eye and hand to achieve balance (do not calculate). Then pick one force and "derive" it from the other three. Perform this experiment five times with five different choices for mass.
* Go to pencil and paper and devise a way to set up the 3-4-5 right triangle. Verify it with a demonstration.
* Search the internet and find some other well-known right triangles with integers and test two more.
# Physics equations/Local anchors and styles
### long arrows and centered equations

<center><math>\begin{matrix}\overrightarrow{v}=\frac{\Delta \overrightarrow{s}}{\Delta t} =\frac{\overrightarrow{s}_{final}-\overrightarrow{s}_{initial}}{t_{final}-t_{initial}}\end{matrix}</math></center>

### Comments to editor

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### Hidden passage

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### links

* https://meta.wikimedia.org/wiki/Help:Displaying_a_formula
* https://en.wikipedia.org/wiki/Help:Wiki_markup
# Physics equations/Physeq
#### SampleName

% This is obsolete:
* Foo
Call with {{#lst:Physics_equations/Equations|SampleName}}
* From Template:Physeq1
# Physics equations/Maxwell's equations

under construction

#### Maxwell's equations integral form

$\oint _{S}{\vec {E}}\cdot \mathrm {d} {\vec {A}}={\frac {1}{\epsilon _{0}}}Q_{enc}$
$\oint _{S}{\vec {B}}\cdot \mathrm {d} {\vec {A}}=0$
$\oint _{C}{\vec {E}}\cdot \mathrm {d} {\vec {\ell }}=-\int _{S}{\frac {\partial {\vec {B}}}{\partial t}}\cdot \mathrm {d} {\vec {A}}$
$\oint _{C}{\vec {B}}\cdot \mathrm {d} {\vec {\ell }}=\mu \int _{S}{\vec {J}}\cdot \mathrm {d} {\vec {A}}+{\frac {1}{c^{2}}}\int _{S}{\frac {\partial {\vec {D}}}{\partial t}}\cdot \mathrm {d} {\vec {A}}$
# Physics equations/Previous exams

* Physics equations/Exams for calculus based first semester course (Summer 2014
* Physics equations/Exams for algebra/trig based second semester course (Spring 2014)
* Physics equations/Exams for calculus based first semester course (Spring 2014)
* Second semester calc F2013
In the future try to follow the paradigm of the bottom of this list
#[[/Second semester calc F2013/]]
# Physics equations/Magnetic forces
## Magnetic forces: Lorentz and Laplace]

https://en.wikipedia.org/w/index.php?title=Magnetic_field&oldid=582423833 The Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force
    ${\vec {F}}=q\left({\vec {E}}+{\vec {v}}\times {\vec {B}}\right)$
(in SI units). Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a particle which might be traveling near the speed of light (relativistic form of the Lorentz force).
If the charged particles are travelling in a wire we have the Laplace force:
    ${\vec {F}}=I\int d{\vec {\ell }}\times {\vec {B}}$
* Problem: A wire segment that is 2.5 meters long carries a current of 12 amps in a 3.5 Tesla field. What is the force on the segment if the angle between the wire and the magnetic field is 30 degrees? *
Since sin 30° = ½, we have
    $\mathbf {F} =\left|I\int d{\boldsymbol {\ell }}\times \mathbf {B} \right|=(12)(2.5)(3.5)(0.5)=52.5{\text{N}}.$

## next ptoble

If $x\neq 0$, then
    $B={\frac {\mu _{0}I}{2}}{\frac {a^{2}}{(x^{2}+a^{2})^{3/2}}}$.
Here only the first (and far simpler) problem is solved. Both variants of the right-hand rule stipulate that each element of length in the line integral contributes an element of magnetic field that points in the same direction, as shown in the figures below: