{"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\/zh\/uncategorized\/online-vector-calculator-for-rotor-balancing\/","title":{"rendered":"\u5728\u7ebf\u8f6c\u5b50\u5e73\u8861\u77e2\u91cf\u8ba1\u7b97\u5668"},"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\">\u77e2\u91cf\u8ba1\u7b97\u5668<\/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    .vc-fields {\n      display: flex;\n      gap: 16px;\n    }\n    .vc-field {\n      flex: 1;\n    }\n    .vc-field-label {\n      font-size: 12px;\n      color: #2563eb;\n      font-weight: 500;\n      display: block;\n      margin-bottom: 4px;\n    }\n    .vc-field input {\n      width: 100%;\n      padding: 12px;\n      border: 1px solid #bfdbfe;\n      border-radius: 4px;\n      text-align: center;\n      font-family: monospace;\n      font-size: 18px;\n    }\n    .vc-field input:focus {\n      outline: none;\n      border-color: #3b82f6;\n      box-shadow: 0 0 0 2px rgba(59,130,246,0.3);\n    }\n    .vc-diagram {\n      display: flex;\n      justify-content: center;\n      margin-top: 12px;\n    }\n    .vc-diagram svg {\n      background: #eff6ff;\n      border-radius: 4px;\n    }\n    .vc-operations {\n      background: #fff;\n      border-radius: 8px;\n      border: 1px solid #bfdbfe;\n      padding: 16px;\n      margin-bottom: 20px;\n    }\n    .vc-operations-label {\n      font-size: 14px;\n      font-weight: 500;\n      color: #1e3a8a;\n      margin-bottom: 12px;\n    }\n    .vc-ops-grid {\n      display: grid;\n      grid-template-columns: repeat(5, 1fr);\n      gap: 8px;\n    }\n    @media (max-width: 500px) {\n      .vc-ops-grid { grid-template-columns: repeat(3, 1fr); }\n    }\n    .vc-op-btn {\n      padding: 12px 8px;\n      border-radius: 4px;\n      border: 1px solid #bfdbfe;\n      background: #eff6ff;\n      color: #1d4ed8;\n      cursor: pointer;\n      text-align: center;\n      transition: all 0.2s;\n    }\n    .vc-op-btn:hover {\n      background: #dbeafe;\n    }\n    .vc-op-btn.active {\n      background: #2563eb;\n      color: #fff;\n      border-color: #2563eb;\n    }\n    .vc-op-icon {\n      font-size: 16px;\n      font-weight: 700;\n    }\n    .vc-op-name {\n      font-size: 11px;\n      margin-top: 4px;\n    }\n    .vc-scalar-row {\n      display: none;\n      margin-top: 16px;\n      justify-content: center;\n      align-items: center;\n      gap: 12px;\n    }\n    .vc-scalar-row.visible {\n      display: flex;\n    }\n    .vc-scalar-row label {\n      font-size: 14px;\n      color: #1d4ed8;\n    }\n    .vc-scalar-row input {\n      width: 80px;\n      padding: 8px;\n      border: 1px solid #bfdbfe;\n      border-radius: 4px;\n      text-align: center;\n      font-family: monospace;\n    }\n    .vc-calc-btn {\n      width: 100%;\n      padding: 14px;\n      background: #2563eb;\n      color: #fff;\n      font-size: 16px;\n      font-weight: 600;\n      border: none;\n      border-radius: 8px;\n      cursor: pointer;\n      transition: background 0.2s;\n    }\n    .vc-calc-btn:hover {\n      background: #1d4ed8;\n    }\n    .vc-result {\n      display: none;\n      margin-top: 20px;\n      padding: 20px;\n      background: #fff;\n      border-radius: 8px;\n      border: 2px solid #93c5fd;\n    }\n    .vc-result.visible {\n      display: block;\n    }\n    .vc-result-label {\n      font-size: 14px;\n      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    .vc-help-section:last-child {\n      margin-bottom: 0;\n    }\n    .vc-help-heading {\n      font-weight: 600;\n      margin-bottom: 8px;\n    }\n    .vc-help-text {\n      color: #1d4ed8;\n      line-height: 1.5;\n    }\n    .vc-help-list {\n      color: #1d4ed8;\n      line-height: 1.6;\n      padding-left: 0;\n      list-style: none;\n    }\n    .vc-help-list li {\n      margin-bottom: 8px;\n    }\n    .vc-help-example {\n      background: #eff6ff;\n      padding: 12px;\n      border-radius: 4px;\n      border: 1px solid #bfdbfe;\n      color: #1e40af;\n      line-height: 1.6;\n    }\n    .vc-help-formulas {\n      font-family: monospace;\n      font-size: 12px;\n      color: #1d4ed8;\n      padding-top: 12px;\n      border-top: 1px solid #eff6ff;\n    }\n  <\/style>\n<\/head>\n<body>\n\n<div class=\"vc-container\">\n  <h1 class=\"vc-title\">\u77e2\u91cf\u8ba1\u7b97\u5668<\/h1>\n\n  <div class=\"vc-inputs\">\n    <div class=\"vc-vector-box\">\n      <div class=\"vc-vector-label\">\u5411\u91cf A<\/div>\n      <div class=\"vc-fields\">\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">\u8d28\u91cf\uff0c\u514b<\/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\">\u89d2\u5ea6\uff0c\u5ea6<\/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\">\u5411\u91cf B<\/div>\n      <div class=\"vc-fields\">\n        <div class=\"vc-field\">\n          <label class=\"vc-field-label\">\u8d28\u91cf\uff0c\u514b<\/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\">\u89d2\u5ea6\uff0c\u5ea6<\/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\">\u64cd\u4f5c<\/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\">\u6dfb\u52a0<\/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\">\u51cf\u53bb<\/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\">\u5bf9\u9762\u7684<\/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\">\u91cf\u7a0b<\/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\uff0cY<\/div>\n      <\/button>\n    <\/div>\n    <div class=\"vc-scalar-row\" id=\"vc-scalar-row\">\n      <label>\u4e58\u6570 k\uff1a<\/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\">\u8ba1\u7b97<\/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>\u8fd9\u4e2a\u8ba1\u7b97\u5668\u7684\u5de5\u4f5c\u539f\u7406<\/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\">\u8fd9\u4e2a\u8ba1\u7b97\u5668\u662f\u505a\u4ec0\u4e48\u7528\u7684\uff1f<\/div>\n      <p class=\"vc-help-text\">\n        \u8be5\u8ba1\u7b97\u5668\u4f7f\u7528\u6781\u5750\u6807\uff08\u5e45\u503c\u548c\u89d2\u5ea6\uff09\u8fdb\u884c\u77e2\u91cf\u8fd0\u7b97\u3002\u5b83\u4e13\u4e3a\u8f6c\u5b50\u5e73\u8861\u5e94\u7528\u800c\u8bbe\u8ba1\uff0c\u5176\u4e2d\u4e0d\u5e73\u8861\u91cf\u4ee5\u7279\u5b9a\u89d2\u5ea6\u4f4d\u7f6e\u7684\u8d28\u91cf\u6765\u8861\u91cf\u3002\u8be5\u8ba1\u7b97\u5668\u6709\u52a9\u4e8e\u5408\u5e76\u591a\u4e2a\u4e0d\u5e73\u8861\u91cf\u8bfb\u6570\u3001\u786e\u5b9a\u6821\u6b63\u914d\u91cd\u7684\u4f4d\u7f6e\u4ee5\u53ca\u8fdb\u884c\u5750\u6807\u7cfb\u8f6c\u6362\u3002.\n      <\/p>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u8f93\u5165\u683c\u5f0f<\/div>\n      <p class=\"vc-help-text\">\n        \u6bcf\u4e2a\u5411\u91cf\u7531\u4e24\u4e2a\u503c\u5b9a\u4e49\uff1a\u8d28\u91cf\uff08\u4ee5\u514b\u6216\u4efb\u610f\u5355\u4f4d\u8868\u793a\uff09\u548c\u89d2\u5ea6\uff08\u4ee5\u5ea6\u4e3a\u5355\u4f4d\uff0c\u8303\u56f4\u4ece 0 \u5230 360\uff09\u3002\u53c2\u8003\u89d2\u5ea6 0\u00b0 \u6307\u5411\u4e0a\u65b9\uff0812 \u70b9\u949f\u4f4d\u7f6e\uff09\uff0c\u89d2\u5ea6\u987a\u65f6\u9488\u65b9\u5411\u9012\u589e\u3002\u8fd9\u4e0e\u5927\u591a\u6570\u5e73\u8861\u4eea\u5668\u7684\u60ef\u4f8b\u4e00\u81f4\uff0c\u5176\u4e2d\u76f8\u4f4d\u53c2\u8003\u901a\u5e38\u6807\u8bb0\u5728\u8f6c\u5b50\u9876\u90e8\u3002.\n      <\/p>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u8fd0\u8425<\/div>\n      <ul class=\"vc-help-list\">\n        <li><strong>\u52a0\u53f7\uff08+\uff09<\/strong> \u2014 \u5c06\u4e24\u4e2a\u5411\u91cf\u5408\u5e76\u6210\u4e00\u4e2a\u7ed3\u679c\u5411\u91cf\u3002\u5f53\u9700\u8981\u8ba1\u7b97\u6765\u81ea\u591a\u4e2a\u6765\u6e90\u7684\u603b\u4e0d\u5e73\u8861\u91cf\uff0c\u6216\u5c06\u4e24\u4e2a\u6821\u6b63\u6743\u91cd\u5408\u5e76\u6210\u4e00\u4e2a\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u6b64\u529f\u80fd\u3002.<\/li>\n        <li><strong>\u51cf\u6cd5\uff08-\uff09<\/strong> \u2014 \u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5dee\u503c\uff08A \u51cf\u53bb B\uff09\u3002\u53ef\u7528\u4e8e\u786e\u5b9a\u6821\u6b63\u540e\u7684\u6b8b\u4f59\u4e0d\u5e73\u8861\u3002.<\/li>\n        <li><strong>\u76f8\u53cd\u65b9\u5411\uff08\u00b1180\u00b0\uff09<\/strong> \u2014 \u5c06\u5411\u91cf A \u7684\u89d2\u5ea6\u52a0\u4e0a 180\u00b0\u3002\u8fd9\u6837\u5c31\u80fd\u786e\u5b9a\u6821\u6b63\u6743\u91cd\u5e94\u8be5\u653e\u7f6e\u7684\u4f4d\u7f6e\u3002.<\/li>\n        <li><strong>\u5c3a\u5ea6\uff08k\u00d7\uff09<\/strong> \u2014 \u5c06\u8d28\u91cf\u4e58\u4ee5\u7cfb\u6570 k\u3002\u5f53\u91cd\u65b0\u8ba1\u7b97\u4e0d\u540c\u5b89\u88c5\u534a\u5f84\u7684\u6821\u6b63\u8d28\u91cf\u65f6\uff0c\u8fd9\u81f3\u5173\u91cd\u8981\uff1am2 = m1 \u00d7 (r1 \/ r2)\u3002.<\/li>\n        <li><strong>\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\uff08X\uff0cY\uff09<\/strong> \u2014 \u5c06\u6781\u5750\u6807\u8f6c\u6362\u4e3a\u7b1b\u5361\u5c14\u5750\u6807\uff1aX = m \u00d7 cos(\u89d2\u5ea6)\uff0cY = m \u00d7 sin(\u89d2\u5ea6)\u3002.<\/li>\n      <\/ul>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u5178\u578b\u5e94\u7528<\/div>\n      <ul class=\"vc-help-list\">\n        <li><strong>\u5355\u5e73\u9762\u5e73\u8861\uff1a<\/strong> \u6d4b\u91cf\u4e0d\u5e73\u8861\u60c5\u51b5\uff0c\u4f7f\u7528\u53cd\u5411\u529f\u80fd\u627e\u5230\u6821\u6b63\u89d2\u5ea6\uff0c\u5b89\u88c5\u914d\u91cd\u5e76\u8fdb\u884c\u9a8c\u8bc1\u3002.<\/li>\n        <li><strong>\u5408\u5e76\u6743\u91cd\uff1a<\/strong> \u4f7f\u7528\u52a0\u6cd5\u8fd0\u7b97\uff0c\u5c06\u4e24\u4e2a\u5df2\u5b89\u88c5\u7684\u6821\u6b63\u914d\u91cd\u66ff\u6362\u4e3a\u4e00\u4e2a\u7b49\u6548\u914d\u91cd\u3002.<\/li>\n        <li><strong>\u534a\u5f84\u8f6c\u6362\uff1a<\/strong> \u5c06\u6821\u6b63\u781d\u7801\u79fb\u52a8\u5230\u4e0d\u540c\u7684\u534a\u5f84\u65f6\uff0c\u4f7f\u7528 Scale \u91cd\u65b0\u8ba1\u7b97\u8d28\u91cf\u3002.<\/li>\n        <li><strong>\u5206\u9879\u91cd\u91cf\uff1a<\/strong> \u5f53\u65e0\u6cd5\u83b7\u5f97\u7cbe\u786e\u89d2\u5ea6\u65f6\uff0c\u5c06\u6821\u6b63\u8d28\u91cf\u5206\u914d\u5230\u4e24\u4e2a\u76f8\u90bb\u7684\u53f6\u7247\u4e0a\u3002.<\/li>\n      <\/ul>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u793a\u4f8b 1\uff1a\u67e5\u627e\u6821\u6b63\u91cd\u91cf\u4f4d\u7f6e<\/div>\n      <div class=\"vc-help-example\">\n        \u5e73\u8861\u4eea\u5668\u663e\u793a\u4e0d\u5e73\u8861 <strong>15\u514b\uff0c72\u00b0<\/strong>.<br><br>\n        \u8f93\u5165\u5411\u91cf A\uff1a\u8d28\u91cf = 15\uff0c\u89d2\u5ea6 = 72<br>\n        \u9009\u62e9 <strong>\u76f8\u53cd\u65b9\u5411\uff08\u00b1180\u00b0\uff09<\/strong> \u7136\u540e\u70b9\u51fb\u201c\u8ba1\u7b97\u201d\u3002.<br><br>\n        \u7ed3\u679c\uff1a <strong>15\u514b\uff0c\u6e29\u5ea6252\u00b0<\/strong><br><br>\n        \u5728 252\u00b0 \u4f4d\u7f6e\u5b89\u88c5\u4e00\u4e2a 15 \u514b\u7684\u6821\u6b63\u914d\u91cd\uff0c\u4ee5\u8865\u507f\u4e0d\u5e73\u8861\u3002.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u4f8b 2\uff1a\u5c06\u4e24\u4e2a\u91cd\u91cf\u5408\u5e76\u4e3a\u4e00\u4e2a<\/div>\n      <div class=\"vc-help-example\">\n        \u7ecf\u8fc7\u591a\u6b21\u5e73\u8861\u8c03\u6574\u540e\uff0c\u8f6c\u5b50\u4e0a\u5b89\u88c5\u4e86\u4e24\u4e2a\u6821\u6b63\u914d\u91cd\uff1a \n        <strong>5\u514b\uff0c30\u00b0<\/strong> \u548c <strong>8\u514b\uff0c75\u00b0<\/strong>. \u4f60\u60f3\u7528\u4e00\u4e2a\u5355\u72ec\u7684\u781d\u7801\u6765\u4ee3\u66ff\u5b83\u4eec\u3002.<br><br>\n        \u8f93\u5165\u5411\u91cf A\uff1a\u8d28\u91cf = 5\uff0c\u89d2\u5ea6 = 30<br>\n        \u8f93\u5165\u5411\u91cf B\uff1a\u8d28\u91cf = 8\uff0c\u89d2\u5ea6 = 75<br>\n        \u9009\u62e9 <strong>\u52a0\u53f7\uff08+\uff09<\/strong> \u7136\u540e\u70b9\u51fb\u201c\u8ba1\u7b97\u201d\u3002.<br><br>\n        \u7ed3\u679c\uff1a <strong>12.05\u514b\uff0c\u6e29\u5ea657.9\u00b0<\/strong><br><br>\n        \u79fb\u9664\u4e24\u4e2a\u914d\u91cd\u5757\uff0c\u5e76\u5728\u5927\u7ea6 58\u00b0 \u7684\u4f4d\u7f6e\u5b89\u88c5\u4e00\u4e2a 12 \u514b\u7684\u914d\u91cd\u5757\u3002\u8fd9\u4e2a\u5355\u72ec\u7684\u914d\u91cd\u5757\u53ef\u4ee5\u4ea7\u751f\u4e0e\u539f\u5148\u4e24\u4e2a\u914d\u91cd\u5757\u7ec4\u5408\u8d77\u6765\u76f8\u540c\u7684\u5e73\u8861\u6548\u679c\u3002.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u4f8b 3\uff1a\u6539\u53d8\u4fee\u6b63\u534a\u5f84<\/div>\n      <div class=\"vc-help-example\">\n        \u5e73\u8861\u7cfb\u7edf\u8ba1\u7b97\u51fa\u7684\u4fee\u6b63\u503c\u4e3a <strong>20\u514b<\/strong> \u534a\u5f84\u4e3a <strong>100\u6beb\u7c73<\/strong>. \u4f46\u662f\uff0c\u4f60\u9700\u8981\u5c06\u914d\u91cd\u5b89\u88c5\u5728\u534a\u5f84\u4e3a <strong>80\u6beb\u7c73<\/strong> \u7531\u4e8e\u7a7a\u95f4\u9650\u5236\u3002.<br><br>\n        \u7531\u4e8e\u5e73\u8861\u6548\u5e94\u53d6\u51b3\u4e8e\u8d28\u91cf\u548c\u534a\u5f84\u7684\u4e58\u79ef\uff08m \u00d7 r = \u5e38\u6570\uff09\uff0c\u56e0\u6b64\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\uff1ak = 100 \/ 80 = 1.25<br><br>\n        \u8f93\u5165\u5411\u91cf A\uff1a\u8d28\u91cf = 20\uff0c\u89d2\u5ea6 = \uff08\u60a8\u7684\u4fee\u6b63\u89d2\u5ea6\uff09<br>\n        \u8bbe\u7f6e\u4e58\u6570 k = 1.25<br>\n        \u9009\u62e9 <strong>\u5c3a\u5ea6\uff08k\u00d7\uff09<\/strong> \u7136\u540e\u70b9\u51fb\u201c\u8ba1\u7b97\u201d\u3002.<br><br>\n        \u7ed3\u679c\uff1a <strong>25\u514b<\/strong> \u4ee5\u76f8\u540c\u7684\u89d2\u5ea6<br><br>\n        \u5728\u8f83\u5c0f\u7684\u534a\u5f84 80 \u6beb\u7c73\u5904\uff0c\u8981\u8fbe\u5230\u76f8\u540c\u7684\u77eb\u6b63\u6548\u679c\uff0c\u9700\u8981 25 \u514b\u800c\u4e0d\u662f 20 \u514b\u3002.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-heading\">\u4f8b 4\uff1a\u5c06\u91cd\u91cf\u5206\u914d\u5230\u4e24\u4e2a\u53f6\u7247\u4e0a<\/div>\n      <div class=\"vc-help-example\">\n        \u6240\u9700\u7684\u66f4\u6b63\u662f <strong>10\u514b\uff0c110\u00b0<\/strong>, \u4f46\u662f\uff0c\u4f60\u53ea\u80fd\u5c06\u914d\u91cd\u8fde\u63a5\u5230\u4f4d\u4e8e\u4ee5\u4e0b\u4f4d\u7f6e\u7684\u98ce\u6247\u53f6\u7247\u4e0a\uff1a <strong>90\u00b0<\/strong> \u548c <strong>126\u00b0<\/strong> \uff085 \u4e2a\u5200\u7247\uff0c\u95f4\u9694 36\u00b0\uff09\u3002.<br><br>\n        \u6821\u6b63\u89d2 110\u00b0 \u4f4d\u4e8e\u8fd9\u4e24\u7247\u53f6\u7247\u4e4b\u95f4\u3002\u8981\u786e\u5b9a\u6bcf\u7247\u53f6\u7247\u5e94\u52a0\u591a\u5c11\u91cd\u91cf\uff0c\n        \u8bf7\u4f7f\u7528\u7cbe\u786e\u7684\u4e09\u89d2\u5206\u914d\u6cd5\uff08\u6309\u89d2\u5ea6\u5bf9\u8d28\u91cf\u8fdb\u884c\u7b80\u5355\u6bd4\u4f8b\u5206\u914d\u53ea\u662f\u4e00\u79cd\u8fd1\u4f3c\uff0c\u4f1a\u4f7f\u5e73\u8861\u8d28\u91cf\u6821\u6b63\u4e0d\u8db3\u51e0\u4e2a\u767e\u5206\u70b9\uff09\uff1a<br><br>\n        \u5230 90\u00b0 \u53f6\u7247\u7684\u89d2\u8ddd\u79bb\uff1a\u03b1 = 110\u00b0 \u2212 90\u00b0 = 20\u00b0<br>\n        \u5230 126\u00b0 \u53f6\u7247\u7684\u89d2\u8ddd\u79bb\uff1a\u03b2 = 126\u00b0 \u2212 110\u00b0 = 16\u00b0<br>\n        \u53f6\u7247\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a\u03b1 + \u03b2 = 36\u00b0<br><br>\n        90\u00b0 \u53f6\u7247\u4e0a\u7684\u914d\u91cd\uff1a10 \u00d7 sin(16\u00b0) \/ sin(36\u00b0) = <strong>4.69 g<\/strong><br>\n        126\u00b0 \u53f6\u7247\u4e0a\u7684\u914d\u91cd\uff1a10 \u00d7 sin(20\u00b0) \/ sin(36\u00b0) = <strong>5.82 g<\/strong><br><br>\n        \u4e3a\u4e86\u9a8c\u8bc1\uff0c\u8bf7\u4f7f\u7528\u52a0\u6cd5\uff1a<br>\n        \u5411\u91cf A\uff1a\u8d28\u91cf = 4.69\uff0c\u89d2\u5ea6 = 90<br>\n        \u5411\u91cf B\uff1a\u8d28\u91cf = 5.82\uff0c\u89d2\u5ea6 = 126<br>\n        \u7ed3\u679c\uff1a <strong>10\u514b\uff0c110\u00b0<\/strong> \u2014 \u7b26\u5408\u539f\u59cb\u8981\u6c42\u3002.\n      <\/div>\n    <\/div>\n\n    <div class=\"vc-help-section\">\n      <div class=\"vc-help-formulas\">\n        <div class=\"vc-help-heading\">\u516c\u5f0f<\/div>\n        \u6781\u5750\u6807\u5230\u7b1b\u5361\u5c14\u5750\u6807\u7684\u8f6c\u6362\uff1aX = m \u00d7 cos(a)\uff0cY = m \u00d7 sin(a)<br>\n        \u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u5230\u6781\u5750\u6807\u7cfb\u7684\u8f6c\u6362\uff1am = sqrt(X\u00b2 + Y\u00b2)\uff0ca = atan2(Y, X)<br>\n        \u534a\u5f84\u4fee\u6b63\uff1am2 = m1 \u00d7 (r1 \/ r2)<br>\n        \u5206\u89e3\u914d\u91cd\uff08\u7cbe\u786e\uff09\uff1am1 = M \u00d7 sin(\u03b2) \/ sin(\u03b1 + \u03b2), m2 = M \u00d7 sin(\u03b1) \/ sin(\u03b1 + \u03b2)\uff0c\u5176\u4e2d \u03b1 \u662f\u4ece\u6821\u6b63\u89d2\u5230\u53f6\u7247 1 \u7684\u89d2\u8ddd\u79bb\uff0c\u03b2 \u662f\u5230\u53f6\u7247 2 \u7684\u89d2\u8ddd\u79bb\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? 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