{"id":20916,"date":"2025-12-20T23:28:00","date_gmt":"2025-12-20T23:28:00","guid":{"rendered":"https:\/\/vibromera.eu\/?p=20916"},"modified":"2025-12-21T17:45:09","modified_gmt":"2025-12-21T17:45:09","slug":"online-vector-calculator-for-rotor-balancing","status":"publish","type":"post","link":"https:\/\/vibromera.eu\/hu\/uncategorized\/online-vector-calculator-for-rotor-balancing\/","title":{"rendered":"Online vektorkalkul\u00e1tor rotor kiegyens\u00falyoz\u00e1shoz"},"content":{"rendered":"<div id=\"pl-20916\"  class=\"panel-layout\" ><div id=\"pg-20916-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-20916-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-20916-0-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"0\" ><h3 class=\"widget-title\">Vektor kalkul\u00e1tor<\/h3><div class=\"textwidget custom-html-widget\"><!DOCTYPE html>\n<html lang=\"en\">\n<head>\n  <meta charset=\"UTF-8\">\n  <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n\n  <style>\n    .vc-container {\n      font-family: -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, sans-serif;\n      max-width: 1400px;\n      margin: 0 auto;\n      padding: 16px;\n      background: #f8fafc;\n      box-sizing: border-box;\n    }\n    .vc-container * {\n      box-sizing: border-box;\n    }\n    .vc-title {\n      text-align: center;\n      font-size: 24px;\n      font-weight: 700;\n      color: #1e3a8a;\n      margin: 0 0 24px 0;\n    }\n    .vc-inputs {\n      display: grid;\n      grid-template-columns: 1fr 1fr;\n      gap: 16px;\n      margin-bottom: 20px;\n    }\n    @media (max-width: 500px) {\n      .vc-inputs { grid-template-columns: 1fr; }\n    }\n    .vc-vector-box {\n      padding: 16px;\n      border-radius: 8px;\n      border: 1px solid #bfdbfe;\n      background: #fff;\n    }\n    .vc-vector-label {\n      font-weight: 500;\n      color: #1e3a8a;\n      margin-bottom: 12px;\n    }\n    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color: #2563eb;\n      font-weight: 500;\n      margin-bottom: 8px;\n    }\n    .vc-result-values {\n      display: flex;\n      justify-content: center;\n      align-items: center;\n      gap: 32px;\n    }\n    .vc-result-item {\n      text-align: center;\n    }\n    .vc-result-num {\n      font-size: 28px;\n      font-family: monospace;\n      font-weight: 700;\n      color: #1e3a8a;\n    }\n    .vc-result-unit {\n      font-size: 12px;\n      color: #3b82f6;\n      margin-top: 4px;\n    }\n    .vc-result-sep {\n      font-size: 24px;\n      color: #93c5fd;\n    }\n    .vc-result-cartesian {\n      text-align: center;\n      font-size: 14px;\n      color: #3b82f6;\n      margin-top: 12px;\n      padding-top: 12px;\n      border-top: 1px solid #eff6ff;\n    }\n    .vc-result-note {\n      text-align: center;\n      font-size: 14px;\n      color: #1d4ed8;\n      background: #eff6ff;\n      padding: 8px;\n      border-radius: 4px;\n      border: 1px solid #bfdbfe;\n      margin-top: 12px;\n    }\n    .vc-result-diagram {\n      display: flex;\n      justify-content: center;\n      margin-top: 12px;\n    }\n    .vc-help-toggle {\n      width: 100%;\n      margin-top: 24px;\n      padding: 12px;\n      background: #fff;\n      border: 1px solid #bfdbfe;\n      border-radius: 8px;\n      color: #1d4ed8;\n      font-size: 14px;\n      font-weight: 500;\n      cursor: pointer;\n      display: flex;\n      justify-content: space-between;\n      align-items: center;\n      transition: background 0.2s;\n    }\n    .vc-help-toggle:hover {\n      background: #eff6ff;\n    }\n    .vc-help-icon {\n      color: #93c5fd;\n    }\n    .vc-help-content {\n      display: none;\n      margin-top: 8px;\n      padding: 16px;\n      background: #fff;\n      border: 1px solid #bfdbfe;\n      border-radius: 8px;\n      font-size: 14px;\n      color: #1e3a8a;\n    }\n    .vc-help-content.visible {\n      display: block;\n    }\n    .vc-help-section {\n      margin-bottom: 20px;\n    }\n   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vektor<\/div>\n      <div class=\"vc-fields\">\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">T\u00f6meg, g<\/label>\n          <input type=\"number\" id=\"vc-mass1\" value=\"10\" step=\"0.1\" min=\"0\">\n        <\/div>\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">Sz\u00f6g, fok<\/label>\n          <input type=\"number\" id=\"vc-angle1\" value=\"45\" step=\"1\">\n        <\/div>\n      <\/div>\n      <div class=\"vc-diagram\">\n        <svg id=\"vc-svg1\" width=\"80\" height=\"80\"><\/svg>\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-vector-box\">\n      <div class=\"vc-vector-label\">B vektor<\/div>\n      <div class=\"vc-fields\">\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">T\u00f6meg, g<\/label>\n          <input type=\"number\" id=\"vc-mass2\" value=\"8\" step=\"0.1\" min=\"0\">\n        <\/div>\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">Sz\u00f6g, fok<\/label>\n          <input type=\"number\" id=\"vc-angle2\" value=\"180\" step=\"1\">\n        <\/div>\n      <\/div>\n      <div class=\"vc-diagram\">\n        <svg id=\"vc-svg2\" width=\"80\" height=\"80\"><\/svg>\n      <\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"vc-operations\">\n    <div class=\"vc-operations-label\">M\u0171velet<\/div>\n    <div class=\"vc-ops-grid\">\n      <button class=\"vc-op-btn active\" data-op=\"add\">\n        <div class=\"vc-op-icon\">+<\/div>\n        <div class=\"vc-op-name\">Add<\/div>\n      <\/button>\n      <button class=\"vc-op-btn\" data-op=\"subtract\">\n        <div class=\"vc-op-icon\">\u2212<\/div>\n        <div class=\"vc-op-name\">Kivon\u00e1s<\/div>\n      <\/button>\n      <button class=\"vc-op-btn\" data-op=\"opposite\">\n        <div class=\"vc-op-icon\">\u00b1180\u00b0<\/div>\n        <div class=\"vc-op-name\">Szemben<\/div>\n      <\/button>\n      <button class=\"vc-op-btn\" data-op=\"scale\">\n        <div class=\"vc-op-icon\">k\u00d7<\/div>\n        <div class=\"vc-op-name\">Sk\u00e1la<\/div>\n      <\/button>\n      <button class=\"vc-op-btn\" data-op=\"cartesian\">\n        <div class=\"vc-op-icon\">\u2192<\/div>\n        <div class=\"vc-op-name\">X, Y<\/div>\n      <\/button>\n    <\/div>\n    <div class=\"vc-scalar-row\" id=\"vc-scalar-row\">\n      <label>k-as szorz\u00f3:<\/label>\n      <input type=\"number\" id=\"vc-scalar\" value=\"2\" step=\"0.1\">\n    <\/div>\n  <\/div>\n\n  <button class=\"vc-calc-btn\" id=\"vc-calc-btn\">Sz\u00e1m\u00edtsa ki a  c\u00edmet.<\/button>\n\n  <div class=\"vc-result\" id=\"vc-result\">\n    <div class=\"vc-result-label\" id=\"vc-result-label\"><\/div>\n    <div class=\"vc-result-values\" id=\"vc-result-values\"><\/div>\n    <div class=\"vc-result-cartesian\" id=\"vc-result-cartesian\"><\/div>\n    <div class=\"vc-result-note\" id=\"vc-result-note\"><\/div>\n    <div class=\"vc-result-diagram\" id=\"vc-result-diagram\"><\/div>\n  <\/div>\n\n  <button class=\"vc-help-toggle\" id=\"vc-help-toggle\">\n    <span>Hogyan m\u0171k\u00f6dik ez a kalkul\u00e1tor<\/span>\n    <span class=\"vc-help-icon\" id=\"vc-help-icon\">+<\/span>\n  <\/button>\n\n  <div class=\"vc-help-content\" id=\"vc-help-content\">\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">Mire val\u00f3 ez a kalkul\u00e1tor?<\/div>\n      <p class=\"vc-help-text\">\n        Ez a sz\u00e1mol\u00f3g\u00e9p vektorm\u0171veleteket v\u00e9gez pol\u00e1rkoordin\u00e1t\u00e1k (nagys\u00e1g \u00e9s sz\u00f6g) seg\u00edts\u00e9g\u00e9vel. Rotor-kiegyens\u00falyoz\u00e1si alkalmaz\u00e1sokhoz tervezt\u00e9k, ahol az egyens\u00falyhi\u00e1nyt egy adott sz\u00f6ghelyzetben l\u00e9v\u0151 t\u00f6megk\u00e9nt m\u00e9rik. A sz\u00e1mol\u00f3g\u00e9p seg\u00edt t\u00f6bb egyens\u00falyhi\u00e1ny-leolvas\u00e1s kombin\u00e1l\u00e1s\u00e1ban, a korrekci\u00f3s s\u00faly elhelyez\u00e9s\u00e9nek meghat\u00e1roz\u00e1s\u00e1ban \u00e9s a koordin\u00e1ta-rendszerek k\u00f6z\u00f6tti \u00e1tv\u00e1lt\u00e1sban.\n      <\/p>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">Beviteli form\u00e1tum<\/div>\n      <p class=\"vc-help-text\">\n        Minden vektort k\u00e9t \u00e9rt\u00e9k hat\u00e1roz meg: t\u00f6meg (grammban vagy tetsz\u0151leges egys\u00e9gben) \u00e9s sz\u00f6g (0-t\u00f3l 360-ig terjed\u0151 fokban). A 0\u00b0-os referenciasz\u00f6g felfel\u00e9 mutat (12 \u00f3r\u00e1s poz\u00edci\u00f3), a sz\u00f6gek pedig az \u00f3ramutat\u00f3 j\u00e1r\u00e1s\u00e1val megegyez\u0151en n\u00f6vekednek. Ez megfelel a legt\u00f6bb kiegyens\u00falyoz\u00f3 m\u0171szer \u00e1ltal haszn\u00e1lt konvenci\u00f3nak, ahol a f\u00e1zisreferenci\u00e1t jellemz\u0151en a rotor tetej\u00e9n jel\u00f6lik.\n      <\/p>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">M\u0171veletek<\/div>\n      <ul class=\"vc-help-list\">\n        <li><strong>\u00d6sszead\u00e1s (+)<\/strong> \u2014 K\u00e9t vektort egyetlen ered\u0151 vektorr\u00e1 egyes\u00edt. Ezt akkor haszn\u00e1lja, ha t\u00f6bb forr\u00e1sb\u00f3l kell meghat\u00e1roznia a teljes egyens\u00falyhi\u00e1nyt, vagy k\u00e9t korrekci\u00f3s s\u00falyt szeretne egyetlen vektorr\u00e1 egyes\u00edteni.<\/li>\n        <li><strong>Kivon\u00e1s (\u2212)<\/strong> \u2014 Kisz\u00e1m\u00edtja k\u00e9t vektor (A m\u00ednusz B) k\u00f6z\u00f6tti k\u00fcl\u00f6nbs\u00e9get. Hasznos a korrekci\u00f3 ut\u00e1ni marad\u00e9k egyens\u00falyhi\u00e1ny meghat\u00e1roz\u00e1s\u00e1hoz.<\/li>\n        <li><strong>Szemben (\u00b1180\u00b0)<\/strong> \u2014 180\u00b0-ot ad az A vektor sz\u00f6g\u00e9hez. Ez megadja azt a poz\u00edci\u00f3t, ahov\u00e1 a korrekci\u00f3s s\u00falyt el kell helyezni.<\/li>\n        <li><strong>Sk\u00e1la (k\u00d7)<\/strong> \u2014 A t\u00f6meget megszorozza k egy\u00fctthat\u00f3val. Alapvet\u0151 fontoss\u00e1g\u00fa a korrekci\u00f3s t\u00f6meg \u00fajrasz\u00e1m\u00edt\u00e1sakor elt\u00e9r\u0151 szerel\u00e9si sug\u00e1r eset\u00e9n: m2 = m1 \u00d7 (r1 \/ r2).<\/li>\n        <li><strong>Descartes-f\u00e9le (X, Y)<\/strong> \u2014 Pol\u00e1rkoordin\u00e1t\u00e1kat konvert\u00e1l der\u00e9ksz\u00f6g\u0171 koordin\u00e1t\u00e1kba: X = m \u00d7 cos(sz\u00f6g), Y = m \u00d7 sin(sz\u00f6g).<\/li>\n      <\/ul>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">Tipikus alkalmaz\u00e1sok<\/div>\n      <ul class=\"vc-help-list\">\n        <li><strong>Egys\u00edk\u00fa kiegyens\u00falyoz\u00e1s:<\/strong> M\u00e9rje meg az egyens\u00falyhi\u00e1nyt, haszn\u00e1lja az Ellent\u00e9tes funkci\u00f3t a korrekci\u00f3s sz\u00f6g megtal\u00e1l\u00e1s\u00e1hoz, helyezzen fel s\u00falyt \u00e9s ellen\u0151rizze.<\/li>\n        <li><strong>S\u00falyok kombin\u00e1l\u00e1sa:<\/strong> Cser\u00e9ljen ki k\u00e9t felszerelt korrekci\u00f3s s\u00falyt egyetlen, azzal egyen\u00e9rt\u00e9k\u0171 s\u00fallyal az \u00f6sszead\u00e1s seg\u00edts\u00e9g\u00e9vel.<\/li>\n        <li><strong>Sug\u00e1r \u00e1tv\u00e1lt\u00e1s:<\/strong> A M\u00e9retez\u00e9s funkci\u00f3val \u00fajrasz\u00e1m\u00edthatja a t\u00f6meget, amikor a korrekci\u00f3s s\u00falyt egy m\u00e1sik sug\u00e1rra helyezi \u00e1t.<\/li>\n        <li><strong>Osztott s\u00falyok:<\/strong> Ha a pontos sz\u00f6g nem \u00e9rhet\u0151 el, ossza el a korrekci\u00f3s t\u00f6meget k\u00e9t szomsz\u00e9dos lap\u00e1t k\u00f6z\u00f6tt.<\/li>\n      <\/ul>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">1. p\u00e9lda: Korrekci\u00f3s s\u00faly poz\u00edci\u00f3j\u00e1nak meghat\u00e1roz\u00e1sa<\/div>\n      <div class=\"vc-help-example\">\n        Egy kiegyens\u00falyoz\u00f3 eszk\u00f6z a k\u00f6vetkez\u0151k egyens\u00falyhi\u00e1ny\u00e1t mutatja: <strong>15 gramm 72\u00b0C-on<\/strong>.<br><br>\n        Adja meg az A vektort: T\u00f6meg = 15, Sz\u00f6g = 72<br>\n        V\u00e1lassza ki <strong>Szemben (\u00b1180\u00b0)<\/strong> \u00e9s kattintson a Sz\u00e1m\u00edt\u00e1s gombra.<br><br>\n        Eredm\u00e9ny: <strong>15 gramm 252\u00b0C-on<\/strong><br><br>\n        Szereljen fel egy 15 grammos korrekci\u00f3s s\u00falyt a 252\u00b0-os poz\u00edci\u00f3ba az egyens\u00falyhi\u00e1ny kompenz\u00e1l\u00e1s\u00e1ra.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">2. p\u00e9lda: K\u00e9t s\u00falyoz\u00e1s egyes\u00edt\u00e9se egybe<\/div>\n      <div class=\"vc-help-example\">\n        T\u00f6bb kiegyens\u00falyoz\u00e1si iter\u00e1ci\u00f3 ut\u00e1n k\u00e9t korrekci\u00f3s s\u00faly van felszerelve a rotorra: \n        <strong>5 gramm 30\u00b0C-on<\/strong> \u00e9s <strong>8 gramm 75\u00b0C-on<\/strong>. Egyetlen s\u00fallyal szeretn\u00e9d \u0151ket helyettes\u00edteni.<br><br>\n        Adja meg az A vektort: T\u00f6meg = 5, Sz\u00f6g = 30<br>\n        Adja meg a B vektort: T\u00f6meg = 8, Sz\u00f6g = 75<br>\n        V\u00e1lassza ki <strong>\u00d6sszead\u00e1s (+)<\/strong> \u00e9s kattintson a Sz\u00e1m\u00edt\u00e1s gombra.<br><br>\n        Eredm\u00e9ny: <strong>12,05 gramm 57,9\u00b0-on<\/strong><br><br>\n        T\u00e1vol\u00edtsd el mindk\u00e9t s\u00falyt, \u00e9s helyezz el egy 12 grammos s\u00falyt k\u00f6r\u00fclbel\u00fcl 58\u00b0-os sz\u00f6gben. Ez az egyetlen s\u00faly ugyanazt az egyens\u00falyoz\u00f3 hat\u00e1st \u00e9ri el, mint az eredeti k\u00e9t s\u00faly egy\u00fcttv\u00e9ve.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">3. p\u00e9lda: Korrekci\u00f3s sug\u00e1r m\u00f3dos\u00edt\u00e1sa<\/div>\n      <div class=\"vc-help-example\">\n        A kiegyenl\u00edt\u0151 rendszer kisz\u00e1m\u00edtotta a k\u00f6vetkez\u0151 korrekci\u00f3t: <strong>20 gramm<\/strong> egy sug\u00e1rra <strong>100 mm<\/strong>. A s\u00falyt azonban a k\u00f6vetkez\u0151 sugar\u00fa k\u00f6rzetben kell elhelyezni: <strong>80 mm<\/strong> a helysz\u0171ke miatt.<br><br>\n        Mivel a kiegyenl\u00edt\u0151 hat\u00e1s a t\u00f6meg \u00e9s a sug\u00e1r szorzat\u00e1t\u00f3l f\u00fcgg (m \u00d7 r = const), \u00fajra kell sz\u00e1molni: k = 100 \/ 80 = 1,25<br><br>\n        Adja meg az A vektort: T\u00f6meg = 20, Sz\u00f6g = (a korrekci\u00f3s sz\u00f6g)<br>\n        \u00c1ll\u00edtsa be a k = 1,25 szorz\u00f3t<br>\n        V\u00e1lassza ki <strong>Sk\u00e1la (k\u00d7)<\/strong> \u00e9s kattintson a Sz\u00e1m\u00edt\u00e1s gombra.<br><br>\n        Eredm\u00e9ny: <strong>25 gramm<\/strong> ugyanabban a sz\u00f6gben<br><br>\n        A kisebb, 80 mm-es sug\u00e1rn\u00e1l 20 gramm helyett 25 grammra van sz\u00fcks\u00e9g ugyanazon korrekci\u00f3 el\u00e9r\u00e9s\u00e9hez.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">4. p\u00e9lda: S\u00falymegoszt\u00e1s k\u00e9t penge k\u00f6z\u00f6tt<\/div>\n      <div class=\"vc-help-example\">\n        A sz\u00fcks\u00e9ges korrekci\u00f3 a <strong>10 gramm 110\u00b0C-on<\/strong>, de s\u00falyokat csak a ventil\u00e1torlap\u00e1tokra r\u00f6gz\u00edthet, amelyek a <strong>90\u00b0<\/strong> \u00e9s <strong>126\u00b0<\/strong> (5 penge, 36\u00b0-os sz\u00f6gben egym\u00e1st\u00f3l).<br><br>\n        A 110\u00b0-os korrekci\u00f3s sz\u00f6g e k\u00e9t lap\u00e1t k\u00f6z\u00e9 esik. Annak meghat\u00e1roz\u00e1s\u00e1hoz, hogy mennyi s\u00faly ker\u00fclj\u00f6n az egyes lap\u00e1tokra, \n        haszn\u00e1lja a pontos trigonometrikus feloszt\u00e1st (a t\u00f6meg sz\u00f6g szerinti egyszer\u0171 ar\u00e1nyos feloszt\u00e1sa csak k\u00f6zel\u00edt\u00e9s, \u00e9s t\u00f6bb sz\u00e1zal\u00e9kkal alulkorrekci\u00f3zza a kiegyens\u00falyoz\u00f3 t\u00f6meget):<br><br>\n        Angular distance to the blade at 90\u00b0: \u03b1 = 110\u00b0 \u2212 90\u00b0 = 20\u00b0<br>\n        Angular distance to the blade at 126\u00b0: \u03b2 = 126\u00b0 \u2212 110\u00b0 = 16\u00b0<br>\n        A lap\u00e1tok k\u00f6z\u00f6tti sz\u00f6g: \u03b1 + \u03b2 = 36\u00b0<br><br>\n        Weight on 90\u00b0 blade: 10 \u00d7 sin(16\u00b0) \/ sin(36\u00b0) = <strong>4.69 g<\/strong><br>\n        Weight on 126\u00b0 blade: 10 \u00d7 sin(20\u00b0) \/ sin(36\u00b0) = <strong>5.82 g<\/strong><br><br>\n        Az ellen\u0151rz\u00e9shez haszn\u00e1ld az \u00d6sszead\u00e1st:<br>\n        Vector A: Mass = 4.69, Angle = 90<br>\n        Vector B: Mass = 5.82, Angle = 126<br>\n        Eredm\u00e9ny: <strong>10 gramm 110\u00b0C-on<\/strong> \u2013 megfelel az eredeti k\u00f6vetelm\u00e9nynek.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-formulas\">\n        <div class=\"vc-help-heading\">K\u00e9pletek<\/div>\n        Pol\u00e1risb\u00f3l der\u00e9ksz\u00f6g\u0171be: X = m \u00d7 cos(a), Y = m \u00d7 sin(a)<br>\n        Descartes-koordin\u00e1t\u00e1b\u00f3l pol\u00e1risba: m = sqrt(X\u00b2 + Y\u00b2), a = atan2(Y, X)<br>\n        Sug\u00e1rkorrekci\u00f3: m2 = m1 \u00d7 (r1 \/ r2)<br>\n        Split weights (exact): m1 = M \u00d7 sin(\u03b2) \/ sin(\u03b1 + \u03b2), m2 = M \u00d7 sin(\u03b1) \/ sin(\u03b1 + \u03b2), where \u03b1 is the angular distance from the correction angle to blade 1 and \u03b2 is the angular distance to blade 2\n      <\/div>\n    <\/div>\n  <\/div>\n<\/div>\n\n<script>\n(function() {\n  let operation = 'add';\n\n  const mass1 = document.getElementById('vc-mass1');\n  const angle1 = document.getElementById('vc-angle1');\n  const mass2 = document.getElementById('vc-mass2');\n  const angle2 = document.getElementById('vc-angle2');\n  const scalarInput = document.getElementById('vc-scalar');\n  const scalarRow = document.getElementById('vc-scalar-row');\n  const calcBtn = document.getElementById('vc-calc-btn');\n  const resultDiv = document.getElementById('vc-result');\n  const resultLabel = document.getElementById('vc-result-label');\n  const resultValues = document.getElementById('vc-result-values');\n  const resultCartesian = document.getElementById('vc-result-cartesian');\n  const resultNote = document.getElementById('vc-result-note');\n  const resultDiagram = document.getElementById('vc-result-diagram');\n  const helpToggle = document.getElementById('vc-help-toggle');\n  const helpContent = document.getElementById('vc-help-content');\n  const helpIcon = document.getElementById('vc-help-icon');\n  const opBtns = document.querySelectorAll('.vc-op-btn');\n\n  function toCartesian(m, angleDeg) {\n    const rad = angleDeg * Math.PI \/ 180;\n    return { x: m * Math.cos(rad), y: m * Math.sin(rad) };\n  }\n\n  function toPolar(x, y) {\n    const m = Math.sqrt(x * x + y * y);\n    let a = Math.atan2(y, x) * 180 \/ Math.PI;\n    if (a < 0) a += 360;\n    return { mass: m, angle: a };\n  }\n\n  function formatNum(n, dec) {\n    dec = dec || 2;\n    if (Math.abs(n) < 0.0001) return '0';\n    return parseFloat(n.toFixed(dec)).toString();\n  }\n\n  function normalizeAngle(a) {\n    while (a < 0) a += 360;\n    while (a >= 360) a -= 360;\n    return a;\n  }\n\n  function drawVector(svgId, m, a, color) {\n    const svg = document.getElementById(svgId);\n    const cx = 40, cy = 40, r = 25;\n    const rad = (a - 90) * Math.PI \/ 180;\n    const ex = cx + r * Math.cos(rad);\n    const ey = cy + r * Math.sin(rad);\n    \n    svg.innerHTML = `\n      <circle cx=\"${cx}\" cy=\"${cy}\" r=\"30\" fill=\"none\" stroke=\"#bfdbfe\" stroke-width=\"1\"\/>\n      <line x1=\"${cx}\" y1=\"${cy}\" x2=\"${cx}\" y2=\"10\" stroke=\"#93c5fd\" stroke-width=\"1\"\/>\n      <text x=\"43\" y=\"9\" font-size=\"8\" fill=\"#3b82f6\">0<\/text>\n      ${m > 0 ? `<line x1=\"${cx}\" y1=\"${cy}\" x2=\"${ex}\" y2=\"${ey}\" stroke=\"${color}\" stroke-width=\"2\"\/>\n      <circle cx=\"${ex}\" cy=\"${ey}\" r=\"3\" fill=\"${color}\"\/>` : ''}\n      <circle cx=\"${cx}\" cy=\"${cy}\" r=\"2\" fill=\"#1e3a8a\"\/>\n    `;\n  }\n\n  function drawResultVector(m, a) {\n    const cx = 50, cy = 50, r = 35;\n    const rad = (a - 90) * Math.PI \/ 180;\n    const ex = cx + r * Math.cos(rad);\n    const ey = cy + r * Math.sin(rad);\n    \n    resultDiagram.innerHTML = `\n      <svg width=\"100\" height=\"100\" style=\"background:#eff6ff;border-radius:4px;\">\n        <circle cx=\"${cx}\" cy=\"${cy}\" r=\"40\" fill=\"none\" stroke=\"#bfdbfe\" stroke-width=\"1\"\/>\n        <line x1=\"${cx}\" y1=\"${cy}\" x2=\"${cx}\" y2=\"10\" stroke=\"#93c5fd\" stroke-width=\"1\"\/>\n        <line x1=\"${cx}\" y1=\"${cy}\" x2=\"90\" y2=\"${cy}\" stroke=\"#93c5fd\" stroke-width=\"1\"\/>\n        <text x=\"52\" y=\"8\" font-size=\"8\" fill=\"#3b82f6\">0<\/text>\n        <text x=\"92\" y=\"53\" font-size=\"8\" fill=\"#3b82f6\">90<\/text>\n        ${m > 0 ? `<line x1=\"${cx}\" y1=\"${cy}\" x2=\"${ex}\" y2=\"${ey}\" stroke=\"#1d4ed8\" stroke-width=\"2\"\/>\n        <circle cx=\"${ex}\" cy=\"${ey}\" r=\"4\" fill=\"#1d4ed8\"\/>` : ''}\n        <circle cx=\"${cx}\" cy=\"${cy}\" r=\"2\" fill=\"#1e3a8a\"\/>\n      <\/svg>\n    `;\n  }\n\n  function updateDiagrams() {\n    const m1 = parseFloat(mass1.value) || 0;\n    const a1 = normalizeAngle(parseFloat(angle1.value) || 0);\n    const m2 = parseFloat(mass2.value) || 0;\n    const a2 = normalizeAngle(parseFloat(angle2.value) || 0);\n    drawVector('vc-svg1', m1, a1, '#1d4ed8');\n    drawVector('vc-svg2', m2, a2, '#1d4ed8');\n  }\n\n  function calculate() {\n    const m1 = parseFloat(mass1.value) || 0;\n    const a1 = normalizeAngle(parseFloat(angle1.value) || 0);\n    const m2 = parseFloat(mass2.value) || 0;\n    const a2 = normalizeAngle(parseFloat(angle2.value) || 0);\n    const k = parseFloat(scalarInput.value) || 1;\n\n    const c1 = toCartesian(m1, a1);\n    const c2 = toCartesian(m2, a2);\n\n    let label = '', mass = 0, angle = 0, cart = null, note = '', isCartesian = false;\n\n    switch (operation) {\n      case 'add':\n        const sumX = c1.x + c2.x;\n        const sumY = c1.y + c2.y;\n        const sumP = toPolar(sumX, sumY);\n        label = 'Sum of vectors A + B';\n        mass = sumP.mass;\n        angle = sumP.angle;\n        cart = { x: sumX, y: sumY };\n        break;\n      case 'subtract':\n        const diffX = c1.x - c2.x;\n        const diffY = c1.y - c2.y;\n        const diffP = toPolar(diffX, diffY);\n        label = 'Difference A \u2212 B';\n        mass = diffP.mass;\n        angle = diffP.angle;\n        cart = { x: diffX, y: diffY };\n        break;\n      case 'opposite':\n        label = 'Correction weight position for vector A';\n        mass = m1;\n        angle = normalizeAngle(a1 + 180);\n        note = 'Place the correction mass at this angle to compensate for imbalance';\n        break;\n      case 'scale':\n        label = 'Vector A \u00d7 ' + k;\n        mass = m1 * k;\n        angle = a1;\n        break;\n      case 'cartesian':\n        label = 'Cartesian coordinates of vector A';\n        isCartesian = true;\n        cart = c1;\n        break;\n    }\n\n    resultDiv.classList.add('visible');\n    resultLabel.textContent = label;\n\n    if (isCartesian) {\n      resultValues.innerHTML = `\n        <div class=\"vc-result-item\">\n          <div class=\"vc-result-num\">X = ${formatNum(cart.x)}<\/div>\n        <\/div>\n        <div class=\"vc-result-item\">\n          <div class=\"vc-result-num\">Y = ${formatNum(cart.y)}<\/div>\n        <\/div>\n      `;\n      resultCartesian.style.display = 'none';\n      resultNote.style.display = 'none';\n      resultDiagram.innerHTML = '';\n    } else {\n      resultValues.innerHTML = `\n        <div class=\"vc-result-item\">\n          <div class=\"vc-result-num\">${formatNum(mass)}<\/div>\n          <div class=\"vc-result-unit\">grams<\/div>\n        <\/div>\n        <div class=\"vc-result-sep\">\/<\/div>\n        <div class=\"vc-result-item\">\n          <div class=\"vc-result-num\">${formatNum(angle, 1)}\u00b0<\/div>\n          <div class=\"vc-result-unit\">angle<\/div>\n        <\/div>\n      `;\n\n      if (cart) {\n        resultCartesian.textContent = 'X = ' + formatNum(cart.x) + ', Y = ' + formatNum(cart.y);\n        resultCartesian.style.display = 'block';\n      } else {\n        resultCartesian.style.display = 'none';\n      }\n\n      if (note) {\n        resultNote.textContent = note;\n        resultNote.style.display = 'block';\n      } else {\n        resultNote.style.display = 'none';\n      }\n\n      drawResultVector(mass, angle);\n    }\n  }\n\n  opBtns.forEach(function(btn) {\n    btn.addEventListener('click', function() {\n      opBtns.forEach(function(b) { b.classList.remove('active'); });\n      btn.classList.add('active');\n      operation = btn.getAttribute('data-op');\n      if (operation === 'scale') {\n        scalarRow.classList.add('visible');\n      } else {\n        scalarRow.classList.remove('visible');\n      }\n    });\n  });\n\n  calcBtn.addEventListener('click', calculate);\n\n  helpToggle.addEventListener('click', function() {\n    if (helpContent.classList.contains('visible')) {\n      helpContent.classList.remove('visible');\n      helpIcon.textContent = '+';\n    } else {\n      helpContent.classList.add('visible');\n      helpIcon.textContent = '\u2212';\n    }\n  });\n\n  mass1.addEventListener('input', updateDiagrams);\n  angle1.addEventListener('input', updateDiagrams);\n  mass2.addEventListener('input', updateDiagrams);\n  angle2.addEventListener('input', updateDiagrams);\n\n  updateDiagrams();\n})();\n<\/script>\n\n<\/body>\n<\/html><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Vector Calculator Vector Calculator Vector A Mass, g Angle, deg Vector B Mass, g Angle, deg Operation + Add \u2212 Subtract \u00b1180\u00b0 Opposite k\u00d7 Scale \u2192 X, Y Multiplier k: Calculate How this calculator works + What is this calculator for? This calculator performs vector operations using polar coordinates (magnitude [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":20918,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ai_generated_summary":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-20916","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/posts\/20916","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/comments?post=20916"}],"version-history":[{"count":5,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/posts\/20916\/revisions"}],"predecessor-version":[{"id":20927,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/posts\/20916\/revisions\/20927"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/media\/20918"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/media?parent=20916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/categories?post=20916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/hu\/wp-json\/wp\/v2\/tags?post=20916"}],"curies":[{"name":"munkaf\u00fczet","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}