/*<<origin*/
@font-face{font-family:'Poppins';font-weight:400;font-style:normal;font-display:swap;src:url('/physics/assets/fonts/poppins-400.woff') format('woff')}
@font-face{font-family:'Poppins';font-weight:500;font-style:normal;font-display:swap;src:url('/physics/assets/fonts/poppins-500.woff') format('woff')}
@font-face{font-family:'Poppins';font-weight:700;font-style:normal;font-display:swap;src:url('/physics/assets/fonts/poppins-700.woff') format('woff')}
@font-face{font-family:'InkGlyphs';font-weight:400;font-style:normal;font-display:swap;src:url('/physics/assets/fonts/inkglyphs-400.woff') format('woff');unicode-range:U+0370-03FF,U+221D,U+2264-2265,U+00B2-00B3,U+00B9,U+2070-2079,U+207B,U+2080-2089,U+0127,U+2096,U+2192,U+207A,U+2153-2154,U+2713,U+2090}
@font-face{font-family:'InkGlyphs';font-weight:700;font-style:normal;font-display:swap;src:url('/physics/assets/fonts/inkglyphs-700.woff') format('woff');unicode-range:U+0370-03FF,U+221D,U+2264-2265,U+00B2-00B3,U+00B9,U+2070-2079,U+207B,U+2080-2089,U+0127,U+2096,U+2192,U+207A,U+2153-2154,U+2713,U+2090}
:root{--ink-bg:#0D1B2A;--ink-text:#F5F5F5;--ink-muted:#84919F;--ink-stroke:#6E7D8C;--ink-cyan:#38B6FF;--ink-purple:#A56EFF;--ink-coral:#EF476F;--ink-amber:#FFB703;--ink-success:#2EA043;--ink-card:rgba(255,255,255,.035);--ink-edge:rgba(245,245,245,.13);--ink-hair:rgba(245,245,245,.09);--navy:var(--ink-bg);--ink:var(--ink-text);--cyan:var(--ink-cyan);--amber:var(--ink-amber);--coral:var(--ink-coral);--grey:var(--ink-stroke);--greytx:var(--ink-muted);--bg:var(--ink-bg);--card:var(--ink-card);--edge:var(--ink-edge);--hair:var(--ink-hair);--space-1:.25rem;--space-2:.5rem;--space-3:.75rem;--space-4:1rem;--space-5:1.5rem;--space-6:2rem;--space-7:3rem;--space-8:4rem;--subject-accent:var(--ink-muted)}[data-subject="physics"]{--subject-accent:var(--ink-cyan)}[data-subject="maths"]{--subject-accent:var(--ink-purple)}[data-subject="biology"]{--subject-accent:var(--ink-coral)}
:root{color-scheme:dark;--wtext:42rem;--wpanel:47rem;--wfig:58rem}
*{box-sizing:border-box;margin:0}
html{scroll-behavior:smooth}
body{background:radial-gradient(1100px 520px at 50% -180px,rgba(56,182,255,.055),transparent 62%) var(--bg);
/* 1.68, not 1.75. The brand guide fixes the body measure at 1.68 and
   biology was built to it, so the three libraries were setting the same
   prose at two different rhythms and a reader moving between them felt
   the page change under them. Approved by George on 13 August 2026;
   the practical effect is roughly one line saved per fifteen, which
   shortens every lesson slightly and changes nothing else. */
color:var(--ink);font-family:'Poppins','InkGlyphs',sans-serif;font-weight:400;line-height:1.68;font-size:1.05rem;
-webkit-font-smoothing:antialiased;display:flex;flex-direction:column;min-height:100vh}
main{flex:1 0 auto}
footer.site{flex-shrink:0}
.wrap{max-width:64rem;margin:0 auto;padding:0 1.2rem}
a{color:var(--cyan);text-decoration:none}
a:hover{text-decoration:underline;text-underline-offset:3px}
main p a,main li a,main dd a{text-decoration:underline;text-underline-offset:3px;text-decoration-thickness:1px}
:focus-visible{outline:2px solid var(--cyan);outline-offset:3px;border-radius:4px}
/* Hidden by clipping rather than by left:-999px. The old technique parks a
   real, laid-out box a thousand pixels to the left of the viewport, and a
   320px sweep for horizontal overflow reports it on every page, because it
   genuinely is a box outside the viewport -- there is no way for a probe to
   tell "deliberately parked offscreen" from "this element is why the page
   scrolls sideways". Clipping to a 1px box at the position it already
   occupies takes it out of that question entirely while keeping it in the
   accessibility tree, focusable, and in the tab order, which is the whole
   job of a skip link. width/height/overflow are the belt to clip-path's
   braces for anything that does not support clip-path. */
.skip{position:absolute;left:.5rem;top:0;width:1px;height:1px;overflow:hidden;
  clip-path:inset(50%);white-space:nowrap;background:var(--bg);padding:0;z-index:9}
.skip:focus{width:auto;height:auto;overflow:visible;clip-path:none;padding:.5rem 1rem}
header.site{border-bottom:1px solid var(--hair);padding:1rem 0;margin-bottom:2.6rem}
header.site .wrap{display:flex;align-items:baseline;gap:1.6rem;flex-wrap:wrap}
.wm{display:flex;align-items:center}
.wm:hover{text-decoration:none}
.wmsvg{height:1.6rem;width:auto;display:block}
.wmsvg path{fill:var(--ink)}
.wmsvg circle{fill:var(--cyan)}
nav.top{margin-left:auto;display:flex;gap:1.4rem;font-weight:500;font-size:.95rem}
nav.top a{color:var(--ink);opacity:.82}
nav.top a:hover{color:var(--cyan);opacity:1;text-decoration:none}
/* No aria-current rule here. There used to be one painting the current item
   cyan, from before the subject accents existed, and brand.SHELL_CSS now
   overrides its colour anyway -- the two selectors tie on specificity and the
   shared one is emitted later. All the old rule still contributed was its
   opacity:1, which the shared rule has taken over, so leaving it would be a
   dead declaration that looks like it decides the active colour. */
main{display:block}
h1{font-weight:700;font-size:clamp(2.05rem,5.4vw,2.9rem);line-height:1.14;letter-spacing:-.012em;text-wrap:balance;margin:.1rem 0 .55rem}
.flourish{margin:.15rem 0 1.15rem}
.flourish svg{width:200px;height:auto;display:block}
h2{font-weight:700;font-size:1.42rem;line-height:1.3;margin:2.9rem 0 .9rem;display:flex;align-items:center;gap:.6rem;text-wrap:balance}
h2::before{content:"";width:.48rem;height:.48rem;border-radius:50%;background:var(--cyan);flex:none}
p{margin:0 0 1.15rem}
strong{font-weight:700}
.lede{color:var(--greytx);font-weight:500;font-size:1.17rem;line-height:1.6;margin-bottom:1.3rem;text-wrap:pretty}
.crumbs{font-size:.85rem;font-weight:500;color:var(--greytx);margin:0 0 1.15rem;letter-spacing:.01em}
.crumbs a{color:var(--greytx)}
/*origin>>*/
.chips{display:flex;gap:.5rem;flex-wrap:wrap;margin:0 0 1.5rem}
.chip{border:1px solid var(--edge);border-radius:99px;padding:.16rem .78rem;font-size:.78rem;font-weight:500;color:var(--greytx);letter-spacing:.02em}
.chip.spec{border-color:rgba(56,182,255,.45);color:var(--cyan)}a.chip.spec{text-decoration:none;display:inline-block;line-height:1.55;min-height:1.9rem;padding-top:.2rem;padding-bottom:.2rem}a.chip.spec:hover,a.chip.spec:focus-visible{border-color:var(--cyan);text-decoration:underline}
.builds{font-size:.9rem;font-weight:500;color:var(--greytx);margin:.35rem 0 1.4rem}
.builds+.builds{margin-top:-.9rem}
.builds a{color:var(--greytx);text-decoration:underline;text-underline-offset:3px}
.goals{border-top:1px solid var(--hair);border-bottom:1px solid var(--hair);padding:1rem 0 .5rem;margin:0 0 1.9rem}
.goals .gl{font-size:.73rem;font-weight:700;letter-spacing:.16em;color:var(--greytx);margin-bottom:.55rem}
.goals ul{list-style:none;margin:0;padding:0}
.goals li{padding:.22rem 0 .22rem 1.25rem;position:relative;color:var(--ink)}
.goals li::before{content:"";position:absolute;left:.1rem;top:.86em;width:.42rem;height:.42rem;border-radius:50%;background:var(--cyan);opacity:.8}
article.lesson>*,article.lesson section.lsec>*{max-width:var(--wtext);margin-left:auto;margin-right:auto;padding-left:1.2rem;padding-right:1.2rem}
article.lesson>section.lsec{max-width:none;padding-left:0;padding-right:0}
article.lesson>.panel,article.lesson section.lsec>.panel{max-width:var(--wpanel)}
article.lesson>.eqs,article.lesson section.lsec>.eqs{max-width:var(--wpanel)}
article.lesson>.rulecard,article.lesson section.lsec>.rulecard{max-width:var(--wpanel)}
article.lesson>.tblwrap,article.lesson section.lsec>.tblwrap{max-width:var(--wpanel)}
article.lesson>.pn,article.lesson section.lsec>.pn{max-width:var(--wpanel)}
article.lesson>figure.fig,article.lesson section.lsec>figure.fig{max-width:var(--wfig)}
/*<<origin*/
/* The same measure, for the pages that are not lessons.
   A lesson is built as <article class="lesson"> straight inside <main>, with
   no .wrap around it, and the six rules above give every one of its children
   a measure. Everything else on the site -- the unit hubs, the tool pages,
   the FAQ, how-to-revise, the exam-board pages, the required practicals --
   is built as <div class="wrap"> inside <main>, and .wrap is 64rem. So the
   same paragraph, written by the same person for the same reader, was set to
   42rem on a lesson page and to about 1024px on a hub page: roughly 2.4 times
   the measure the brand guide asks for, and about 150 characters a line on a
   laptop, which is where a reader starts losing their place returning to the
   left margin. .lede in particular is set at 1.17rem and was running the full
   64rem on every hub in the library.
   This is deliberately a list of element selectors rather than a blanket
   `main>.wrap>*`, because the things that must keep the full width are also
   direct children of .wrap: the card grids, the figure blocks, the table
   wrappers, the search box, the flashcard and question-practice bars, the
   board panels. Naming the prose is the version that cannot squeeze one of
   those by accident later.
   margin-right:auto with no margin-left keeps the text block against the left
   edge, lined up with the grids and figures below it. Centring it, the way a
   lesson centres its column, would leave a hub page with a centred paragraph
   sitting over a full-width row of cards, and the two would not share an
   edge anywhere. */
main>.wrap>p,main>.wrap>h1,main>.wrap>h2,main>.wrap>h3,main>.wrap>h4,
main>.wrap>ul,main>.wrap>ol,main>.wrap>dl,main>.wrap>blockquote,
main>.wrap>.hubguide,main>.wrap>.faq,
main>.wrap>.rpsec>p,main>.wrap>.rpsec>h2,main>.wrap>.rpsec>ul,
main>.wrap>.rpsec>.rpwarn,main>.wrap>.rpsec>.rpmark,
main>.wrap>section.qr>p,main>.wrap>section.qr>h2{max-width:var(--wtext);margin-right:auto}
/* Equations need more room than prose does, and get exactly the allowance a
   lesson gives them, for the same reason: a definition list of equations on a
   unit hub is the same content as .eqs inside a lesson. */
main>.wrap>dl.hubeq{max-width:var(--wpanel)}
/* Not prose, and squeezing them is a real cost rather than a neutral one.
   .jumps and .azjump are rows of pill links, .cklegend is a horizontal key,
   .chips is a row of specification chips, and ul.topics is an index whose
   rows carry a coverage tag after the title. All four are laid out across the
   width on purpose and wrap to more lines the narrower they get, which is
   worse to use, not better to read. They are <p> and <ul> elements, so the
   rule above catches them and this one lets them go again. */
main>.wrap>.jumps,main>.wrap>.azjump,main>.wrap>.cklegend,
main>.wrap>.chips,main>.wrap>ul.topics{max-width:none}
/*origin>>*/
.panel{border:1px solid var(--edge);background:var(--card);border-radius:20px;padding:1.25rem 1.45rem 1.15rem;margin:2rem auto}
.panel .pl{display:flex;align-items:center;gap:.6rem;font-size:.73rem;font-weight:700;letter-spacing:.16em;margin-bottom:.6rem}
.pi{width:1.05rem;height:1.05rem;flex:none}
.p-lie{border-color:rgba(239,71,111,.4);background:rgba(239,71,111,.06)}
.p-lie .pl{color:var(--coral)}
.p-exam{border-color:rgba(255,183,3,.38);background:rgba(255,183,3,.05)}
.p-exam .pl{color:var(--amber)}
.p-check{border-color:rgba(56,182,255,.4);background:rgba(56,182,255,.055)}
.p-check .pl{color:var(--cyan)}
.p-check details+details{margin-top:.6rem}
.p-ex .pl{color:var(--ink)}
.p-ex .ext{font-weight:700;margin-bottom:.8rem}
.panel p:last-child{margin-bottom:0}
.p-exam ul{list-style:none;margin:.2rem 0 0;padding:0}
.p-exam li{margin:.7rem 0;padding-left:1.35rem;position:relative}
.p-exam li::before{content:"";position:absolute;left:.05rem;top:.62em;width:.5rem;height:.5rem;border-radius:50%;background:var(--amber)}
details summary{cursor:pointer;display:inline-flex;align-items:center;gap:.55rem;font-weight:500;color:var(--cyan);
border:1px solid rgba(56,182,255,.45);border-radius:11px;padding:.5rem 1.05rem;list-style:none;user-select:none;
transition:background .18s,border-color .18s}
details summary::-webkit-details-marker{display:none}
details summary::after{content:"";width:.5rem;height:.5rem;border-right:2px solid var(--cyan);border-bottom:2px solid var(--cyan);
transform:rotate(45deg) translateY(-1px);transition:transform .18s}
details[open] summary::after{transform:rotate(-135deg) translateY(-2px)}
details summary:hover{background:rgba(56,182,255,.08)}
details[open] summary{margin-bottom:.9rem}
details.hintbox summary{color:var(--greytx);border-color:var(--edge)}
details.hintbox summary::after{border-color:var(--greytx)}
details.hintbox summary:hover{background:rgba(245,245,245,.05)}
figure.fig{margin:2.3rem auto;position:relative}
figure.fig svg{width:100%;height:auto;display:block}
figure.fig img{width:100%;height:auto;display:block}
/* The unit-hub guide, below the lesson links: a reference block, not a
   second lede, so it is ruled off and set a little tighter. */
.hubguide{border-top:1px solid var(--hair);margin-top:2.4rem;padding-top:.6rem}
.hubguide h2{font-size:1.06rem;margin:1.5rem 0 .4rem}
.hubguide ul{margin:.3rem 0 0;padding-left:1.1rem}
.hubguide li{margin:0 0 .45rem;line-height:1.6}
.hubeq{margin:.4rem 0 0}
.hubeq dt{font-weight:700;margin:.7rem 0 .1rem}
/* A hub equation row is .ieq, which is white-space:nowrap, and often
   carries two equations with a \qquad between them. On a 390px phone
   five of the physics unit hubs pushed the whole page sideways --
   508px on mechanics. The row scrolls within itself now, the same
   treatment a dense figure gets, and fig.js gives it a focus stop and
   a name only while it is actually overflowing. */
.hubeq dt{overflow-x:auto;-webkit-overflow-scrolling:touch}
.hubeq dt:focus-visible{outline:2px solid var(--cyan);outline-offset:2px}
.hubeq dd{margin:0 0 0 0;color:var(--greytx);line-height:1.5}
/* The expand control lives in the caption row below the artwork, never over
   it, and keeps a 44px hit target: 2.75rem at the 16px root. */
.figxbtn{flex:none;margin-left:auto;align-self:center;width:2.75rem;height:2.75rem;border-radius:12px;border:1px solid var(--edge);background:var(--bg);color:var(--greytx);cursor:pointer;display:flex;align-items:center;justify-content:center;padding:0;opacity:.85}
.figxbtn:hover{color:var(--cyan);border-color:var(--cyan);opacity:1}
.figxbtn svg{width:1.05rem;height:1.05rem}
/* A figure whose smallest label would project below 9 CSS px on a phone keeps
   a build-computed minimum artwork width (--figmin) and scrolls sideways
   instead of shrinking its labels past reading size. fig.js makes the
   viewport a named, keyboard-focusable region only while it actually
   overflows, so it is never a tab stop that goes nowhere. */
.figscroll{overflow-x:auto;-webkit-overflow-scrolling:touch}
.figscroll svg{min-width:var(--figmin,0)}
.figscroll:focus-visible{outline:2px solid var(--cyan);outline-offset:2px}
dialog.figdlg{background:var(--bg);border:1px solid var(--edge);border-radius:20px;padding:0;width:min(96vw,1150px);max-height:92vh;margin:auto;color:var(--ink)}
dialog.figdlg[open]{display:flex;flex-direction:column}
dialog.figdlg::backdrop{background:rgba(4,10,17,.82)}
.figdlgbar{display:flex;align-items:center;gap:1rem;justify-content:space-between;padding:.55rem .55rem .55rem .95rem;border-bottom:1px solid var(--hair)}
.figdlgbar p{margin:0;font-size:.85rem;color:var(--greytx);line-height:1.35}
.figdlgclose{flex:none;border:1px solid var(--edge);background:none;color:var(--ink);font:inherit;font-size:.85rem;border-radius:12px;padding:.35rem .8rem;cursor:pointer}
.figdlgclose:hover{border-color:var(--cyan);color:var(--cyan)}
.figdlgpan{overflow:auto;flex:1;min-height:0;padding:.9rem;-webkit-overflow-scrolling:touch}
.figdlgpan svg{width:900px;max-width:none;display:block;margin:0 auto}
@media print{.figxbtn,dialog.figdlg{display:none}}
figure.fig figcaption{display:flex;gap:.7rem;align-items:baseline;border-top:1px solid var(--hair);
margin-top:.7rem;padding-top:.55rem;color:var(--greytx);font-size:.9rem;line-height:1.55}
figure.fig .fign{color:var(--cyan);font-weight:700;font-size:.74rem;letter-spacing:.14em;flex:none}
.figsvg .sk-ink{stroke:var(--ink)}.figsvg .sk-cyan{stroke:var(--cyan)}.figsvg .sk-grey{stroke:var(--grey)}
.figsvg .sk-amber{stroke:var(--amber)}.figsvg .sk-coral{stroke:var(--coral)}.figsvg .sk-bg{stroke:var(--bg)}
.figsvg .fl-ink{fill:var(--ink)}.figsvg .fl-cyan{fill:var(--cyan)}.figsvg .fl-grey{fill:var(--grey)}
.figsvg .fl-amber{fill:var(--amber)}.figsvg .fl-coral{fill:var(--coral)}.figsvg .fl-bg{fill:var(--bg)}
rect.fl-bg[stroke-width]{stroke:var(--ink)}
.figsvg text{font-family:'InkGlyphs','Poppins',sans-serif}
.qbar{text-decoration:overline}
/* The combining overline that travels with the clipboard: kept in the text
   flow so copy picks it up, collapsed so the CSS bar above is the only one
   drawn. display:none would remove it from the clipboard as well. */
.qbarc{font-size:0;speak:never}
@keyframes an-swing{from{transform:translate(var(--ox),var(--oy)) rotate(var(--a0)) translate(var(--nox),var(--noy))}to{transform:translate(var(--ox),var(--oy)) rotate(var(--a1)) translate(var(--nox),var(--noy))}}
.an-swing{animation:an-swing 1.9s ease-in-out infinite alternate}
@keyframes an-flip{from{transform:translate(var(--ox),var(--oy)) scaleY(1) translate(var(--nox),var(--noy))}to{transform:translate(var(--ox),var(--oy)) scaleY(-1) translate(var(--nox),var(--noy))}}
.an-flip{animation:an-flip 1.4s ease-in-out infinite alternate}
@keyframes an-jit{0%{transform:translate(0,0)}25%{transform:translate(3.5px,-2.6px)}50%{transform:translate(-2.9px,1.9px)}75%{transform:translate(1.9px,3.2px)}100%{transform:translate(0,0)}}
.an-jit1{animation:an-jit 1.1s linear infinite}
.an-jit2{animation:an-jit 1.6s linear infinite reverse}
.an-jit3{animation:an-jit 2.3s linear infinite}
@keyframes an-walk{0%{transform:translate(0,0)}13%{transform:translate(8px,-5px)}26%{transform:translate(3px,7px)}40%{transform:translate(-7px,11px)}55%{transform:translate(-12px,2px)}68%{transform:translate(-4px,-9px)}82%{transform:translate(6px,-12px)}100%{transform:translate(0,0)}}
.an-walk{animation:an-walk 8.5s linear infinite}
@keyframes an-strike{0%{transform:translate(0,0)}40%{transform:translate(var(--sx),var(--sy))}52%{transform:translate(calc(var(--sx)*0.86),calc(var(--sy)*0.86))}64%{transform:translate(var(--sx),var(--sy))}76%{transform:translate(calc(var(--sx)*0.3),calc(var(--sy)*0.3))}100%{transform:translate(0,0)}}
.an-strike{animation:an-strike 2.6s linear infinite}
@media (prefers-reduced-motion: reduce){.figsvg g[class^="an-"]{animation:none !important;transform:none !important}}
.figsvg .tx-ink{fill:var(--ink)}.figsvg .tx-cyan{fill:var(--cyan)}.figsvg .tx-grey{fill:var(--greytx)}
.figsvg .tx-amber{fill:var(--amber)}.figsvg .tx-coral{fill:var(--coral)}.figsvg .sk-greytx{stroke:var(--greytx)}.figsvg .fl-greytx{fill:var(--greytx)}
@media (prefers-reduced-motion: reduce){.animfig *{animation:none !important}}
@media print{.animfig *{animation:none !important}}
/* Figures animated through the global an-* classes must print still too. */
@media print{.figsvg g[class^="an-"]{animation:none !important;transform:none !important}}
.eqs{text-align:center;padding:.4rem .2rem .2rem;margin:1.9rem auto;overflow-x:auto;overflow-y:hidden}
.eqs .eq{display:block;font-size:clamp(1.15rem,4.6vw,1.5rem);font-weight:500;letter-spacing:.01em;line-height:1.35;white-space:nowrap}
.eqs .dstag{display:inline-block;margin-top:.7rem;font-size:.68rem;font-weight:700;letter-spacing:.15em;
border-radius:99px;padding:.22rem .8rem}
.eqs .ds-on{color:var(--amber);border:1px solid rgba(255,183,3,.45)}
.eqs .ds-off{color:var(--greytx);border:1px solid var(--edge)}
.ieq{font-weight:500;white-space:nowrap}
/* The two semantic twins of an equation: the MathML a screen reader reads and
   the linear text a copy takes. Hidden by clipping and taken out of the flow,
   not by display:none or visibility:hidden, either of which would drop the
   MathML out of the accessibility tree along with the pixels.

   Out of the flow is the load-bearing part. Hiding an inline twin in place
   with font-size:0 reads the same and copies the same, but Chromium still
   gives a <math> containing an <mfrac> a two-pixel minimum width, and two
   pixels beside an inline equation move the rest of the line. Absolute
   positioning is the only version that is provably zero. */
.eqml,.eqtx{position:absolute;width:1px;height:1px;margin:-1px;padding:0;border:0;
overflow:hidden;clip:rect(0 0 0 0);clip-path:inset(50%);white-space:nowrap}
/* Only the visual layer that has a semantic twin opts out of selection, so a
   copy takes the unambiguous .eqtx once instead of the picture and the MathML
   twice. Bare affixes ("R{{_{2}}}") carry no aria-hidden and stay selectable. */
.eqml,.eq[aria-hidden],.ieq[aria-hidden]{-webkit-user-select:none;user-select:none}
.frac{display:inline-flex;flex-direction:column;align-items:center;vertical-align:middle;line-height:1.25;margin:0 .1em}
.frac .n{border-bottom:1.6px solid currentColor;padding:0 .28em}
.frac .d{padding:0 .28em}
.rt{margin-right:.05em}
.rad{border-top:1.6px solid currentColor;padding:0 .15em}
.rt.big{font-size:2.05em;font-weight:400;line-height:1;vertical-align:middle;margin-right:.02em}
.rad.tall{display:inline-flex;align-items:center;vertical-align:middle;border-top:1.6px solid currentColor;padding:.12em .22em .12em .12em}
sup,sub{line-height:0}
.tblwrap{overflow-x:auto;margin:1.6rem auto}
.dtable{width:100%;border-collapse:collapse;font-size:.95rem}
.dtable th{font-size:.73rem;letter-spacing:.14em;text-transform:uppercase;color:var(--greytx);text-align:left;padding:.5rem .8rem;border-bottom:2px solid rgba(110,125,140,.5);font-weight:700}
.dtable td{padding:.55rem .8rem;border-bottom:1px solid rgba(110,125,140,.28)}
.dtable td:first-child{font-weight:700}
.rulecard{border:2px solid rgba(56,182,255,.55);border-radius:20px;text-align:center;padding:1.6rem 1.3rem;margin:2.7rem auto 0}
.rulecard p{margin:0;font-weight:700;font-size:clamp(1.1rem,3.6vw,1.32rem);line-height:1.5}
.rulecard .r2{color:var(--cyan)}
.videotop{margin:.9rem 0 0;font-size:.95rem}
.videotop .pi{width:.85rem;height:.85rem;vertical-align:-.1em;margin-right:.4rem}
.videotop a{color:var(--cyan);text-decoration:underline;text-underline-offset:3px}
.next{display:inline-flex;align-items:center;gap:.6rem;border:1px solid var(--edge);border-radius:14px;
padding:.7rem 1.2rem;color:var(--ink);font-weight:500;transition:border-color .18s,transform .18s cubic-bezier(.2,.9,.3,1.25)}
.next:hover{border-color:var(--cyan);text-decoration:none;transform:translateY(-1px)}
.next svg{width:1rem;height:1rem;flex:none}
.pn{display:flex;gap:.9rem;justify-content:space-between;flex-wrap:wrap;margin:2.4rem auto 0}
.pn .next{max-width:100%}
.pn .rev svg{transform:scaleX(-1)}
.pn .pnl{font-size:.68rem;font-weight:700;letter-spacing:.15em;color:var(--greytx);display:block}
/*<<origin*/
.cards{display:grid;grid-template-columns:repeat(auto-fill,minmax(13.5rem,1fr));gap:.95rem;margin:1.5rem 0}
.card{border:1px solid var(--edge);background:var(--card);border-radius:20px;padding:1.05rem 1.15rem;color:var(--ink);display:block;transition:transform .18s cubic-bezier(.2,.9,.3,1.25),border-color .18s}
a.card:hover{transform:translateY(-2px);border-color:rgba(56,182,255,.5);text-decoration:none}
.card h3,.card h2{font-size:1.02rem;font-weight:700;margin:0 0 .25rem}
/* The first card or section on an index page is an H2, not an H3: a page that
   goes H1 -> H3 leaves a hole in the outline a screen reader has to guess at.
   The level is semantics; the size is this rule. Anywhere a card-level H2
   appears it must lose the section dot and the flex row an H2 normally gets. */
.card h2,.rpcard h2,.cklesson h2,.ki h2,.eqgrp h2{display:block;line-height:1.3;gap:0;letter-spacing:normal}
.card h2::before,.rpcard h2::before,.cklesson h2::before,.ki h2::before,.eqgrp h2::before{content:none;display:none}
.card .meta{color:var(--greytx);font-size:.84rem;font-weight:500}
/*origin>>*/
ul.topics{list-style:none;padding:0;margin:.8rem 0}
ul.topics li{padding:.62rem .2rem;border-bottom:1px solid var(--hair);display:flex;align-items:baseline;gap:.7rem;flex-wrap:wrap}
ul.topics .tag{font-size:.7rem;font-weight:700;letter-spacing:.12em;color:var(--greytx);border:1px solid var(--edge);border-radius:6px;padding:.06rem .48rem;flex:none}
ul.topics .writing{color:var(--greytx)}
.search{width:100%;background:var(--card);border:1px solid var(--edge);border-radius:12px;color:var(--ink);font:inherit;padding:.62rem .95rem;margin:.4rem 0 .8rem}
.search::placeholder{color:var(--greytx)}
.unitline{color:var(--greytx);font-weight:700;font-size:.78rem;letter-spacing:.14em;margin:1.5rem 0 .1rem}
h2.unitline{display:block;line-height:1.5}
h2.unitline::before{display:none}
.jumps{color:var(--greytx);font-size:.88rem;line-height:2;margin:.2rem 0 1.2rem}
.jumps a{color:var(--greytx);text-decoration:underline;text-underline-offset:3px;white-space:nowrap}
.jumps a:hover{color:var(--cyan)}
ul.topics .tag a{text-decoration:none;display:inline-block;padding:.3rem .25rem;min-height:24px;box-sizing:border-box}
ul.topics .tag a:hover{color:var(--cyan);text-decoration:underline;text-underline-offset:3px}
@media (max-width:560px){
.jumps{line-height:2.35}
.jumps a{display:inline-block;border:1px solid var(--edge);border-radius:99px;padding:0 .68rem;text-decoration:none;margin:0 .06rem;line-height:1.9}
ul.topics li.flt{display:block}
ul.topics li.flt .tag{display:table;margin-top:.45rem;font-size:.74rem}
ul.topics li.flt .tag a{padding:.4rem .3rem}
ul.topics li.flt .meta{display:block;color:var(--greytx);font-size:.84rem;margin-top:.3rem}
}
.progress{color:var(--greytx);font-size:.95rem;font-weight:500;margin:-.5rem 0 1.2rem}
/* The origin's own page styles used to sit here and are now in brand.py,
   as ORIGIN_PAGE_CSS. Nothing under /physics/ ever used one of them: the
   family hero, the three subject cards and the library list belong to the
   root, and carrying them here put roughly 3.3 kB of unreachable CSS on
   every physics page. This marked region stays, empty apart from this
   note, because ORIGIN_CSS is assembled from these regions in order and
   this is where that block has to land in the cascade. */
/*<<origin*/
/*origin:page*/
/*origin>>*/
.hero{text-align:center;padding:2.4rem 0 1rem}
.hero .bigwm{margin:0 0 .1rem;display:flex;justify-content:center}
.hero .bigwm .wmsvg{height:clamp(2.85rem,9.4vw,4.35rem)}
/* 1.5rem, not the 1.2rem this rule carried, and the extra .3rem is the only
   thing left of the standing-wave strip that used to sit here. The hero is
   four things in a column: the wordmark, this tagline, the sub-copy and the
   actions. The wordmark and the tagline are one group, bound by the .45rem
   above; the sub-copy is the next group and needs to look like it, so the
   gap above it has to beat the 1.15rem a paragraph leaves below itself.
   With the old 1.2rem the sub-copy sat equidistant between the brand line
   and the buttons and belonged to neither. Nothing else moved: the strip
   was removed rather than replaced, because the brand guide allows no large
   subject motif on a subject homepage, and the standing wave announced
   waves on a page that is about the whole subject. */
.hero .tag{color:var(--greytx);font-weight:500;font-size:1.14rem;margin:.45rem 0 1.5rem}
.hero .links{display:flex;gap:.85rem;justify-content:center;flex-wrap:wrap}
.hero .links2{margin-top:.75rem}
.hero .links2 .btn{font-size:.9rem;padding:.45rem .95rem;color:var(--greytx)}
.hero .links2 .btn:hover{color:var(--ink)}
/* background is not decoration here. .btn was written for anchors, which
   are transparent by default, and it sets a colour without one — so the
   four <button class=btn> controls on the account page took the user
   agent's own button face, which is near-white, and wore near-white
   text on it. "Save settings", "Sync now", "Sign out on this device"
   and "Delete this account" were all legible only by their shape.
   Transparent keeps every anchor exactly as it was and removes the
   default face from every button. */
/* 12px is the radius every button and every input on this site now carries.
   The brand guide sets a 10-12px band for controls and this sheet had drifted
   all over it and below it: .45rem (7.2px) on the checklist bar, the flashcard
   bar, the flashcard grades, the flashcard nav and the option clear; 8px on
   the figure dialog close and the worked-example next; 9px on the figure
   expand; .6rem (9.6px) on the lesson-step nav, the flashcard detail row and
   the option panel. None of those differences meant anything -- they are what
   a stylesheet looks like after two years of somebody typing a plausible
   number each time -- and a reader with a dozen controls in front of them
   reads a dozen slightly different corners as sloppiness rather than as
   grouping. .btn and .searchbox input were already at 12px, so they set the
   value the rest moved to rather than the other way round. Panels are a
   separate band and are capped at 20px; the only 22px left is .fccard, which
   is a genuine major interactive card rather than a static panel. */
.btn{background:transparent;border:1px solid var(--edge);border-radius:12px;padding:.58rem 1.15rem;font-weight:500;color:var(--ink);transition:border-color .18s,transform .18s cubic-bezier(.2,.9,.3,1.25)}
.btn:hover{border-color:var(--cyan);text-decoration:none;transform:translateY(-1px)}
.btn.primary{border-color:var(--cyan);color:var(--cyan)}
.searchbox input{width:100%;max-width:34rem;padding:.62rem .9rem;border-radius:12px;border:1px solid var(--edge);background:transparent;color:var(--ink);font:inherit}
.searchbox input:focus{border-color:var(--cyan)}
.searchbox input::placeholder{color:var(--greytx)}
/* One select, one shape, everywhere on the site.
   Before this rule there was no `appearance` declaration anywhere in the
   physics stylesheet, so every <select> on the site was drawn by the browser
   in its own default face -- near-white on macOS and Windows, on pages whose
   every other control is a dark card with a hairline border -- and the two
   rules that did exist disagreed with each other. Flashcards had .82rem text
   in .35rem/.5rem padding at a 7.2px radius; question practice had .92rem
   text in .3rem/.5rem padding at an 8px radius. Two different control shapes
   for the same job in the same subject, and the account page's two selects
   had no rule at all.
   The chevron is drawn with two linear-gradients rather than an inline SVG
   data: URI, because the Content-Security-Policy sets img-src 'self' and CSS
   background images are governed by img-src. A data: URI would have meant
   adding `data:` to img-src, which is widening the policy to buy a triangle,
   and that trade is not worth making. Gradients cost nothing and need no
   directive.
   appearance:none removes only the painted face. The element is still a
   <select>, so the keyboard behaviour -- typeahead, arrow keys, Home/End, the
   native drop-down list -- is untouched, and the :focus-visible ring defined
   at the top of this sheet still applies because nothing here sets outline. */
select{appearance:none;-webkit-appearance:none;font:inherit;font-size:.88rem;
  padding:.42rem 2rem .42rem .7rem;border-radius:12px;border:1px solid var(--edge);
  background-color:var(--card);color:var(--ink);cursor:pointer;max-width:100%;
  background-image:linear-gradient(45deg,transparent 50%,var(--greytx) 50%),
    linear-gradient(135deg,var(--greytx) 50%,transparent 50%);
  background-position:calc(100% - 1.05rem) calc(50% - 1px),calc(100% - .7rem) calc(50% - 1px);
  background-size:.35rem .35rem,.35rem .35rem;background-repeat:no-repeat}
select:hover{border-color:var(--cyan)}
.wbblock{margin:2.4rem 0 0;padding:1.4rem 1.5rem;border:1px solid var(--edge);border-radius:20px;background:var(--card)}
.wbblock .gl{font-size:.72rem;letter-spacing:.14em;color:var(--cyan);font-weight:600;margin:0 0 .5rem}
.wbblock>p{margin:0 0 1rem;color:var(--greytx)}
.wbblock .cards{grid-template-columns:repeat(auto-fit,minmax(210px,1fr))}
/* A card inside a panel must not repaint the panel's own surface. Both
   carry --card, which is a translucent white over the navy, so a workbook
   card sitting in a workbook block stacked two tints and lifted the ground
   under it from the navy the palette assumes to a lighter grey. Muted text
   on that doubled surface measures 4.49:1, which fails WCAG AA for body
   text by a hundredth, and on the single surface it is 4.96:1 and passes.
   Fixing the nesting rather than the colour keeps both approved tokens
   exactly as the brand guide sets them, and it follows the guide's own
   rule that a surface inside a surface is told apart by its border rather
   than by a second fill. Nothing else on the site stacks two translucent
   backgrounds: a browser sweep of every element on twelve pages across the
   three libraries found this one nesting and no other. */
.wbblock .card{background:transparent}

.card.wb h3{display:flex;align-items:center;gap:.4rem}
.card.wb h3 .pi{width:1rem;height:1rem;flex:none}
/*<<origin*/
.note{color:var(--greytx);font-size:.88rem;margin:2.4rem auto 0}
footer.site{border-top:1px solid var(--hair);margin-top:3.4rem;padding:1.5rem 0 2.3rem;color:var(--greytx);font-size:.86rem}
footer.site a{color:var(--greytx);text-decoration:underline;text-underline-offset:3px}
footer.site .reg{font-size:.78rem;opacity:.8}
/* animation, not just transition. This reset used to stop transitions alone,
   which meant a reader who had asked their operating system for no motion
   still got the 6px slide-and-fade of @keyframes exin on every worked-example
   step, and the 26px horizontal slide of stepr/stepl on every lesson-step
   move in the installed app. Both are keyframe animations, so neither was
   touched. Biology's sheet has had animation:none!important here all along;
   this brings physics into line with it.
   The educational animations inside diagrams are content rather than
   interface, and they are already handled separately and earlier, by the
   two rules on .figsvg g[class^="an-"] and .animfig * near the figure CSS.
   Those rules stop them under the same media query and keep them stopped for
   print, so this blanket rule agrees with them rather than overriding them --
   there is no case where a diagram animates for a reduced-motion reader
   before this change and stops after it, or the reverse. */
@media (prefers-reduced-motion:reduce){*{animation:none!important;transition:none!important;scroll-behavior:auto}}
@media (max-width:680px){header.site .wrap{flex-wrap:wrap;row-gap:.4rem}nav.top{width:100%;margin-left:0;flex-wrap:wrap;justify-content:space-between;gap:.4rem .9rem;font-size:.9rem}}
/* The print block, whose core is brand.PRINT_CSS. It has to be concatenated
   in rather than referenced, because this region is also sliced out to build
   the origin's stylesheet and the origin needs the same treatment on paper.
   The hide list stays here: what to suppress when printing is genuinely per
   subject, and only physics has a video line. */
@media print{
:root{--bg:#ffffff;--ink:#15222e;--cyan:#0b6fae;--amber:#8a6100;--coral:#b3264e;--grey:#5a6570;--greytx:#5a6570;--card:#ffffff;--edge:#c9d1d8;--hair:#dfe5ea}
body{background:#fff;font-size:11pt;line-height:1.55}
a{color:inherit;text-decoration:none}
figure.fig,.panel,.eqs,.goals{break-inside:avoid;page-break-inside:avoid}
details{display:block}details summary{display:none}details>*{display:block}
.card{box-shadow:none}
header.site nav.top,.search,.searchbox,.videotop,.pn,footer.site .fgroups,.hero .links{display:none}
.wbblock .card.wb{box-shadow:none}
}
/*origin>>*/
.ckbar{display:flex;gap:.55rem;flex-wrap:wrap;margin:.2rem 0 1rem}.ckbar button{font:inherit;font-size:.82rem;padding:.4rem .8rem;border:1px solid var(--edge);border-radius:12px;background:var(--card);color:var(--ink);cursor:pointer}.ckbar button:hover{border-color:var(--cyan)}.ckbar button[aria-pressed=true]{border-color:var(--cyan);color:var(--cyan)}.cklegend{font-size:.8rem;color:var(--greytx);margin:.1rem 0 1.5rem}.cklegend span{white-space:nowrap;margin-right:1rem;line-height:2}.cklegend i{display:inline-flex;align-items:center;justify-content:center;font-style:normal;font-weight:700;font-size:.5rem;color:#0D1B2A;width:.72rem;height:.72rem;border-radius:50%;margin-right:.32rem;vertical-align:middle;box-sizing:border-box}.cklist{list-style:none;padding:0;margin:.2rem 0}li.ck{display:flex;gap:.65rem;align-items:flex-start;padding:.28rem 0}li.ck.hide{display:none}.ckdot{flex:0 0 auto;width:1.3rem;height:1.3rem;margin-top:.1rem;border-radius:50%;border:2px solid var(--grey);background:transparent;cursor:pointer;padding:0;position:relative;transition:background .12s,border-color .12s}.ckdot::before{content:'';position:absolute;inset:-12px}.ckdot::after{position:absolute;inset:0;display:flex;align-items:center;justify-content:center;font-size:.76rem;font-weight:700;color:#0D1B2A;line-height:1}.ckdot:hover{border-color:var(--cyan)}li.ck[data-state="1"] .ckdot{background:var(--coral);border-color:var(--coral)}li.ck[data-state="1"] .ckdot::after{content:"!"}li.ck[data-state="2"] .ckdot{background:var(--amber);border-color:var(--amber)}li.ck[data-state="2"] .ckdot::after{content:"~"}li.ck[data-state="3"] .ckdot{background:#2ea043;border-color:#2ea043}li.ck[data-state="3"] .ckdot::after{content:"\2713"}.cktext{flex:1;line-height:1.45}.cktally{display:block;font-size:.8rem;color:var(--greytx);font-weight:400;letter-spacing:0;margin-top:.2rem}.cklesson{margin:0 0 1.15rem}.cklesson h3,.cklesson h2{margin:.1rem 0;font-size:1.02rem}.ckspec{font-size:.76rem;color:var(--greytx);font-weight:400;margin-left:.15rem}.ckstrip{margin-top:2.2rem;padding-top:1.3rem;border-top:1px solid var(--hair)}.ckstrip .cknote{font-size:.85rem;margin-top:.75rem}.nextsteps{margin-top:2.2rem;padding-top:1.3rem;border-top:1px solid var(--hair)}.nextsteps ul{margin:.55rem 0 0;padding-left:1.1rem}.nextsteps li{margin:0 0 .45rem;line-height:1.55}.qr dl{margin:0 0 .5rem}.qr dt{font-weight:700;margin:1.15rem 0 .15rem;color:var(--ink)}.qr dd{margin:0;line-height:1.5}.qr dd .eg{display:block;color:var(--greytx);font-size:.9rem;margin-top:.15rem}.ki{margin:0 0 1rem}.ki h3{margin:.1rem 0 .25rem;font-size:1.0rem}.ki ul{list-style:none;padding:0;margin:0}.ki li{padding:.1rem 0 .1rem .9rem;border-left:2px solid var(--edge);margin:.32rem 0;line-height:1.45}.ub{border-bottom:1px solid var(--edge)}.ub>summary::-webkit-details-marker{display:none}.ub>summary::after{content:'';margin-left:auto;flex:none;width:.5rem;height:.5rem;border-right:2px solid var(--greytx);border-bottom:2px solid var(--greytx);transform:rotate(45deg);transition:transform .18s ease;align-self:center}.ub[open]>summary::after{transform:rotate(-135deg)}.ub>summary:hover .ubt,.ub>summary:focus-visible .ubt{color:var(--cyan)}.ubt{font-weight:600;color:var(--ink)}.ubm{color:var(--greytx);font-size:.86rem}.ubn{color:var(--greytx);font-size:.74rem;font-weight:700;letter-spacing:.1em;border:1px solid var(--edge);border-radius:6px;padding:.06rem .48rem;flex:none;white-space:nowrap}.ubb{padding:.1rem 0 1.1rem}.fltbar{position:sticky;top:0;z-index:5;background:var(--bg);padding:.7rem 0 .5rem;margin:0 0 .4rem}.fltcount{display:flex;gap:.6rem;justify-content:space-between;margin:.35rem .1rem 0;font-size:.78rem;color:var(--greytx)}.fcgo{display:flex;flex-wrap:wrap;align-items:center;gap:.5rem .9rem;margin:.7rem 0 .2rem}.fcstart{font-weight:700;font-size:1rem;padding:.62rem 1.5rem;border-radius:999px;background:var(--cyan);color:var(--navy);border:0;cursor:pointer;min-height:44px}.fcstart:disabled{background:none;color:var(--greytx);border:1px solid var(--edge);cursor:default}.fcstart:hover{filter:brightness(1.08)}.fclink2{background:none;border:0;color:var(--greytx);font-size:.9rem;cursor:pointer;padding:.5rem .1rem;text-decoration:underline;text-underline-offset:3px;min-height:44px}.fclink2:hover,.fclink2:focus-visible{color:var(--cyan)}.fcman{margin:.5rem 0 0}.fcman>summary{cursor:pointer;color:var(--greytx);font-size:.84rem;padding:.45rem .1rem;min-height:44px;display:flex;align-items:center}.fcman>summary:hover{color:var(--cyan)}.azjump a:hover,.azjump a:focus-visible{color:var(--cyan)}@media print{.fltbar{display:none}.ub>summary::after{display:none}}.ki h2{margin:.1rem 0 .25rem;font-size:1.0rem}.ub>summary{display:flex;align-items:baseline;flex-wrap:wrap;gap:.2rem .6rem;cursor:pointer;padding:.85rem .2rem;list-style:none;min-height:44px;box-sizing:border-box}.azjump{display:flex;flex-wrap:wrap;gap:.1rem .55rem;margin:.2rem .1rem 1.2rem;font-size:.84rem;font-weight:700}.azjump a{color:var(--greytx);text-decoration:none;padding:.15rem .1rem}@media print{.azjump{display:none}}.bdwrap{margin:0}.bdsel{border:0;margin:1.4rem 0 0;padding:0;min-width:0}.bdsel>legend{padding:0;margin:0 0 .6rem;font-weight:700;color:var(--ink)}.bdopts{display:flex;flex-wrap:wrap;gap:.5rem}.bdr{position:absolute;width:1px;height:1px;margin:-1px;padding:0;overflow:hidden;clip:rect(0 0 0 0);clip-path:inset(50%);white-space:nowrap;border:0}.bdopts label{display:inline-flex;align-items:center;min-height:44px;box-sizing:border-box;padding:.4rem 1.15rem;border:1px solid var(--edge);border-radius:999px;cursor:pointer;color:var(--greytx);font-size:.94rem;font-weight:600}.bdopts 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