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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>2026南通二模物理T11思考</title>
<script>
MathJax = { tex: {inlineMath: [['$', '$'], ['\\(', '\\)']]} };
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<style>
body {
display: flex; flex-direction: column; align-items: center; justify-content: center;
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f0f2f5; margin: 0; padding: 20px; box-sizing: border-box;
min-height: 100vh; overflow-x: hidden;
}
.container {
background-color: white; padding: 25px; border-radius: 12px;
box-shadow: 0 10px 40px rgba(0,0,0,0.1); display: flex; flex-direction: column;
gap: 20px; width: 100%; max-width: 1400px; box-sizing: border-box;
}
@media (min-width: 1000px) {
.container { flex-direction: row; align-items: flex-start; justify-content: center; }
}
.canvas-wrapper { display: flex; justify-content: center; align-items: center; width: 100%; min-height: 0; }
@media (min-width: 1000px) {
.canvas-wrapper { flex: 1; justify-content: center; padding-right: 20px; }
}
canvas {
background-color: #ffffff; border: 1px solid #dee2e6; border-radius: 8px;
cursor: grab; width: 100%;
max-width: min(1000px, 75vh);
aspect-ratio: 1 / 1;
touch-action: none; box-shadow: inset 0 0 10px rgba(0,0,0,0.02);
user-select: none; -webkit-user-select: none;
}
canvas:active { cursor: grabbing; }
.sidebar { display: flex; flex-direction: column; width: 100%; }
@media (min-width: 1000px) {
.sidebar { flex: 0 0 380px; padding-left: 20px; border-left: 1px solid #e9ecef;}
}
.tabs { display: flex; border-bottom: 2px solid #dee2e6; margin-bottom: 15px; }
.tab-btn {
flex: 1; padding: 12px; background: none; border: none; border-bottom: 3px solid transparent;
font-size: 15px; font-weight: bold; cursor: pointer; color: #6c757d; transition: 0.2s;
}
.tab-btn:hover { color: #495057; background: #f8f9fa; }
.tab-btn.active { color: #0d6efd; border-bottom-color: #0d6efd; }
.tab-content { display: none; flex-direction: column; gap: 15px; }
.tab-content.active { display: flex; }
.control-group { background: #f8f9fa; padding: 15px; border-radius: 8px; border: 1px solid #e9ecef; display: flex; flex-direction: column; gap: 5px; }
label { font-size: 14px; font-weight: 600; color: #495057; display: flex; justify-content: space-between;}
input[type=range] { width: 100%; cursor: pointer;}
.global-buttons { display: flex; gap: 8px; margin-bottom: 10px;}
button.action-btn { flex: 1; padding: 10px; font-size: 14px; font-weight: bold; cursor: pointer; color: white; border: none; border-radius: 6px; transition: 0.2s; background-color: #0d6efd;}
button.action-btn:hover { background-color: #0b5ed7; }
button.action-btn.play { background-color: #198754; }
button.action-btn.reset { background-color: #ffc107; color: #212529; }
.problem-text { font-size: 14px; line-height: 1.6; color: #333; background: #f8f9fa; padding: 12px; border-radius: 6px; margin: 0; border-left: 4px solid #0d6efd;}
.option-btn {
text-align: left; padding: 12px 15px; font-size: 14px; line-height: 1.4;
background: #fff; border: 1px solid #dee2e6; border-radius: 6px;
cursor: pointer; transition: 0.2s; color: #495057; margin-bottom: 8px;
}
.option-btn:hover { background: #e9ecef; }
.option-btn.selected { background: #e7f1ff; border-color: #0d6efd; color: #084298; font-weight: bold; box-shadow: 0 0 0 2px rgba(13, 110, 253, 0.25);}
.option-btn.correct { background: #d1e7dd; border-color: #198754; color: #0f5132;}
.option-btn.wrong { background: #f8d7da; border-color: #dc3545; color: #842029;}
.explanation-box {
display: none; padding: 15px; background: #fff3cd; border: 1px solid #ffecb5; border-left: 4px solid #ffc107;
border-radius: 6px; font-size: 14px; line-height: 1.6; color: #664d03; margin-top: 5px;
animation: fadeIn 0.3s ease-in-out;
}
@keyframes fadeIn { from { opacity: 0; transform: translateY(-5px); } to { opacity: 1; transform: translateY(0); } }
.legend div { font-size: 13px; margin-bottom: 6px; display: flex; align-items: center;}
.legend span { display: inline-block; width: 14px; height: 3px; margin-right: 8px; }
</style>
</head>
<body>
<div class="container">
<div class="canvas-wrapper">
<canvas id="simCanvas" width="1000" height="1000"></canvas>
</div>
<div class="sidebar">
<h3 style="margin-top: 0; margin-bottom: 15px; color: #212529; text-align: center;">2026南通二模物理T11思考</h3>
<div class="global-buttons">
<button id="playBtn" class="action-btn play">▶ 开始运动</button>
<button id="resetBtn" class="action-btn reset">↺ 初始位置 (复位)</button>
<button id="clearBtn" class="action-btn" style="background:#dc3545;">🗑 清空轨迹</button>
</div>
<div class="tabs">
<button id="tabSimBtn" class="tab-btn active" onclick="switchTab('sim')">⚙️ 自由探索</button>
<button id="tabProbBtn" class="tab-btn" onclick="switchTab('prob')">📖 原题互动</button>
</div>
<div id="tabSim" class="tab-content active">
<div class="control-group">
<label>转动方向:</label>
<div style="display: flex; gap: 20px; margin-top: 5px;">
<label style="font-weight: normal; cursor: pointer;"><input type="radio" name="direction" value="-1" checked> 逆时针</label>
<label style="font-weight: normal; cursor: pointer;"><input type="radio" name="direction" value="1"> 顺时针</label>
</div>
</div>
<div class="control-group">
<label>小齿轮半径 (r): <span id="rValue">150</span></label>
<input type="range" id="rSlider" min="50" max="280" step="1" value="150">
<small style="color:#6c757d; font-size:12px;">大齿轮固定为 300 (卡尔丹圆 r=150)</small>
</div>
<div class="control-group">
<label>运行速度 ($\omega$): <span id="speedValue">0.008</span></label>
<input type="range" id="speedSlider" min="0.001" max="0.03" step="0.001" value="0.008">
</div>
<div class="control-group legend">
<label style="cursor: pointer; font-weight: normal; margin-bottom: 10px;"><input type="checkbox" id="showVectors" checked> 显示平行四边形矢量合成</label>
<label style="cursor: pointer; font-weight: normal; margin-bottom: 10px;"><input type="checkbox" id="showTrace" checked> 绘制运动轨迹</label>
<label style="cursor: pointer; font-weight: normal; margin-bottom: 10px; color: #dc3545;"><input type="checkbox" id="showAccel"> 显示加速度矢量 $\vec{a}_P$</label>
<div style="margin-top: 10px;">
<div><span style="background-color: #0d6efd;"></span> $\vec{v}_C$ (牵连速度)</div>
<div><span style="background-color: #fd7e14;"></span> $\vec{v}_{P/C}$ (相对速度)</div>
<div><span style="background-color: #198754; height: 4px;"></span> $\vec{v}_P$ (绝对线速度)</div>
<div><span style="background-color: #dc3545; height: 4px;"></span> $\vec{a}_P$ (绝对加速度)</div>
</div>
</div>
</div>
<div id="tabProb" class="tab-content">
<p class="problem-text">
<strong>题目：</strong>小齿轮的直径与大齿轮的半径相等，P为小齿轮边缘上一点。图示时刻小齿轮贴着左下内壁无滑动滚动。以下判断正确的是：
</p>
<button class="option-btn" id="optA" onclick="selectOption('A')">A. 图示时刻点 P 的速度方向指向 O</button>
<button class="option-btn" id="optB" onclick="selectOption('B')">B. 图示时刻点 P 的加速度方向指向 C</button>
<button class="option-btn" id="optC" onclick="selectOption('C')">C. 点 P 的运动周期是点 C 的两倍</button>
<button class="option-btn" id="optD" onclick="selectOption('D')">D. PO 之间的距离越小，点 P 的加速度越大</button>
<div id="explanationBox" class="explanation-box"></div>
</div>
</div>
</div>
<script>
const canvas = document.getElementById('simCanvas');
const ctx = canvas.getContext('2d');
const playBtn = document.getElementById('playBtn');
const resetBtn = document.getElementById('resetBtn');
const clearBtn = document.getElementById('clearBtn');
const rSlider = document.getElementById('rSlider');
const speedSlider = document.getElementById('speedSlider');
const showVectors = document.getElementById('showVectors');
const showTrace = document.getElementById('showTrace');
const showAccel = document.getElementById('showAccel');
const directionRadios = document.getElementsByName('direction');
const explanationBox = document.getElementById('explanationBox');
const optionBtns = document.querySelectorAll('.option-btn');
const width = canvas.width;
const height = canvas.height;
const cx = width / 2;
const cy = height / 2;
const R = 300;
const INITIAL_THETA = Math.PI * 0.75;
let r = parseInt(rSlider.value);
let omega = parseFloat(speedSlider.value);
let theta = INITIAL_THETA;
let phi_0 = 0;
let isPlaying = false;
let tracePath = [];
let isDraggingP = false;
let currentPx = 0, currentPy = 0;
function switchTab(tabId) {
document.getElementById('tabSim').classList.remove('active');
document.getElementById('tabProb').classList.remove('active');
document.getElementById('tabSimBtn').classList.remove('active');
document.getElementById('tabProbBtn').classList.remove('active');
if(tabId === 'sim') {
document.getElementById('tabSim').classList.add('active');
document.getElementById('tabSimBtn').classList.add('active');
explanationBox.style.display = 'none';
optionBtns.forEach(btn => btn.className = 'option-btn');
} else {
document.getElementById('tabProb').classList.add('active');
document.getElementById('tabProbBtn').classList.add('active');
rSlider.value = 150;
updateParams();
resetToProblemState();
}
}
function getDirection() {
for (const radio of directionRadios) if (radio.checked) return parseInt(radio.value);
return -1;
}
function resetToProblemState() {
isPlaying = false;
playBtn.innerText = "▶ 开始运动"; playBtn.style.backgroundColor = "#198754"; playBtn.style.color = "#fff";
theta = INITIAL_THETA;
phi_0 = 0;
r = 150;
tracePath = [];
showVectors.checked = true;
showAccel.checked = false;
directionRadios[0].checked = true;
drawFrame();
}
function selectOption(opt) {
optionBtns.forEach(btn => btn.className = 'option-btn');
const selectedBtn = document.getElementById('opt' + opt);
let explHtml = "";
switch(opt) {
case 'A':
selectedBtn.classList.add('selected', 'correct');
resetToProblemState();
explHtml = "<strong>解析 A (正确)：</strong>画面已为您定格。接触点是瞬心，结合几何关系可知点 $P$ 轨迹是穿过圆心 $O$ 的直线。目前绿色<strong>速度矢量 $\\vec{v}_P$ 精确沿水平直线指向圆心 $O$</strong>。";
break;
case 'B':
selectedBtn.classList.add('selected', 'wrong');
resetToProblemState();
showAccel.checked = true;
drawFrame();
explHtml = "<strong>解析 B (错误)：</strong>画面已定格，并为您绘制了<strong>红色加速度矢量 $\\vec{a}_P$</strong>。点 $P$ 做简谐运动，其加速度总是指向平衡位置（大圆圆心 $O$），而不是指向小圆圆心 $C$。";
break;
case 'C':
selectedBtn.classList.add('selected', 'wrong');
resetToProblemState();
showTrace.checked = true;
isPlaying = true;
playBtn.innerText = "⏸ 暂停运动"; playBtn.style.backgroundColor = "#ffc107"; playBtn.style.color = "#000";
explHtml = "<strong>解析 C (错误)：</strong>请观察正在播放的动画。圆心 $C$ 绕 $O$ 旋转一整圈（一个周期）的时间内，点 $P$ 刚好在直线上完成一次从一端到另一端再返回的过程。<strong>两者的周期是相等的</strong>（$T_P = T_C$）。";
break;
case 'D':
selectedBtn.classList.add('selected', 'wrong');
resetToProblemState();
showAccel.checked = true;
isPlaying = true;
playBtn.innerText = "⏸ 暂停运动"; playBtn.style.backgroundColor = "#ffc107"; playBtn.style.color = "#000";
explHtml = "<strong>解析 D (错误)：</strong>请观察红色的加速度箭头。根据简谐运动 $a = \\omega^2 x$，距离 $PO$ 越小（越靠近中心），受到的回复力越小，<strong>红色的加速度箭头会变得越短</strong>。当到达中心时加速度为零。";
break;
}
explanationBox.innerHTML = explHtml;
explanationBox.style.display = 'block';
if (window.MathJax) { MathJax.typesetPromise([explanationBox]); }
}
rSlider.addEventListener('input', updateParams);
speedSlider.addEventListener('input', updateParams);
for (const radio of directionRadios) radio.addEventListener('change', () => { tracePath = []; if(!isPlaying) drawFrame(); });
showVectors.addEventListener('change', drawFrame);
showAccel.addEventListener('change', drawFrame);
showTrace.addEventListener('change', drawFrame);
clearBtn.addEventListener('click', () => { tracePath = []; if(!isPlaying) drawFrame(); });
resetBtn.addEventListener('click', resetToProblemState);
playBtn.addEventListener('click', () => {
isPlaying = !isPlaying;
if(isPlaying) {
playBtn.innerText = "⏸ 暂停运动"; playBtn.style.backgroundColor = "#ffc107"; playBtn.style.color = "#000";
} else {
playBtn.innerText = "▶ 开始运动"; playBtn.style.backgroundColor = "#198754"; playBtn.style.color = "#fff";
}
});
function getEventPos(e) {
const rect = canvas.getBoundingClientRect();
return {
x: (e.clientX - rect.left) * (canvas.width / rect.width),
y: (e.clientY - rect.top) * (canvas.height / rect.height)
};
}
canvas.addEventListener('pointerdown', function(e) {
const pos = getEventPos(e);
if (Math.hypot(pos.x - currentPx, pos.y - currentPy) < 60) {
isDraggingP = true;
canvas.setPointerCapture(e.pointerId);
if (e.cancelable) e.preventDefault();
}
});
canvas.addEventListener('pointermove', function(e) {
if (!isDraggingP) return;
if (e.cancelable) e.preventDefault();
const pos = getEventPos(e);
const cx_small = cx + (R - r) * Math.cos(theta);
const cy_small = cy + (R - r) * Math.sin(theta);
phi_0 = Math.atan2(pos.y - cy_small, pos.x - cx_small) + ((R - r) / r) * theta;
tracePath = [];
if (!isPlaying) drawFrame();
});
canvas.addEventListener('pointerup', function(e) {
if (isDraggingP) {
isDraggingP = false;
canvas.releasePointerCapture(e.pointerId);
}
});
canvas.addEventListener('pointercancel', function(e) {
isDraggingP = false;
});
function updateParams() {
r = parseInt(rSlider.value);
omega = parseFloat(speedSlider.value);
document.getElementById('rValue').innerText = r;
document.getElementById('speedValue').innerText = omega.toFixed(3);
if(!isDraggingP) tracePath = [];
if(!isPlaying) drawFrame();
}
function drawArrow(fromX, fromY, toX, toY, color, lineWidth = 2) {
if (Math.abs(fromX - toX) < 0.1 && Math.abs(fromY - toY) < 0.1) return;
const headlen = 12; const angle = Math.atan2(toY - fromY, toX - fromX);
ctx.beginPath(); ctx.moveTo(fromX, fromY); ctx.lineTo(toX, toY);
ctx.lineTo(toX - headlen * Math.cos(angle - Math.PI / 6), toY - headlen * Math.sin(angle - Math.PI / 6));
ctx.moveTo(toX, toY); ctx.lineTo(toX - headlen * Math.cos(angle + Math.PI / 6), toY - headlen * Math.sin(angle + Math.PI / 6));
ctx.strokeStyle = color; ctx.lineWidth = lineWidth; ctx.stroke();
}
function drawFrame() {
ctx.clearRect(0, 0, width, height);
ctx.beginPath(); ctx.arc(cx, cy, R, 0, Math.PI * 2); ctx.strokeStyle = '#343a40'; ctx.lineWidth = 3; ctx.stroke();
ctx.beginPath(); ctx.arc(cx, cy, 6, 0, Math.PI * 2); ctx.fillStyle = '#000'; ctx.fill();
ctx.fillText("O", cx - 25, cy + 20); ctx.font = "20px Arial";
const cx_small = cx + (R - r) * Math.cos(theta);
const cy_small = cy + (R - r) * Math.sin(theta);
const dir = getDirection();
const vcx = -(R - r) * (dir * omega) * Math.sin(theta);
const vcy = (R - r) * (dir * omega) * Math.cos(theta);
const alpha = -((R - r) / r) * theta + phi_0;
const omega_rel = -((R - r) / r) * (dir * omega);
currentPx = cx_small + r * Math.cos(alpha);
currentPy = cy_small + r * Math.sin(alpha);
const vpcx = -omega_rel * (currentPy - cy_small);
const vpcy = omega_rel * (currentPx - cx_small);
const vpx = vcx + vpcx; const vpy = vcy + vpcy;
if (isPlaying && !isDraggingP && showTrace.checked) {
tracePath.push({x: currentPx, y: currentPy});
// 数组上限提升至 50000，基本不会再消失了
if (tracePath.length > 50000) tracePath.shift();
}
if (showTrace.checked && tracePath.length > 0) {
ctx.beginPath(); ctx.moveTo(tracePath[0].x, tracePath[0].y);
for (let i = 1; i < tracePath.length; i++) ctx.lineTo(tracePath[i].x, tracePath[i].y);
ctx.strokeStyle = 'rgba(220, 53, 69, 0.4)'; ctx.lineWidth = 3; ctx.stroke();
}
ctx.beginPath(); ctx.arc(cx_small, cy_small, r, 0, Math.PI * 2); ctx.strokeStyle = 'rgba(13, 110, 253, 0.5)'; ctx.lineWidth = 2.5; ctx.stroke();
ctx.beginPath(); ctx.moveTo(cx, cy); ctx.lineTo(cx_small, cy_small); ctx.lineTo(currentPx, currentPy); ctx.strokeStyle = '#adb5bd'; ctx.lineWidth = 1.5; ctx.stroke();
ctx.beginPath(); ctx.arc(cx_small, cy_small, 6, 0, Math.PI * 2); ctx.fillStyle = '#0d6efd'; ctx.fill();
ctx.fillStyle = '#0d6efd'; ctx.fillText("C", cx_small - 25, cy_small + 25);
ctx.beginPath(); ctx.arc(currentPx, currentPy, isDraggingP ? 15 : 10, 0, Math.PI * 2); ctx.fillStyle = isDraggingP ? '#ffc107' : '#198754'; ctx.fill(); ctx.strokeStyle = '#fff'; ctx.lineWidth = 3; ctx.stroke();
ctx.fillStyle = '#198754'; ctx.fillText("P", currentPx + 15, currentPy - 15);
if (showVectors.checked) {
const v_scale = 65;
drawArrow(currentPx, currentPy, currentPx + vcx * v_scale, currentPy + vcy * v_scale, '#0d6efd', 3);
drawArrow(currentPx, currentPy, currentPx + vpcx * v_scale, currentPy + vpcy * v_scale, '#fd7e14', 3);
ctx.beginPath(); ctx.setLineDash([7, 7]);
ctx.moveTo(currentPx + vcx * v_scale, currentPy + vcy * v_scale); ctx.lineTo(currentPx + vpx * v_scale, currentPy + vpy * v_scale);
ctx.moveTo(currentPx + vpcx * v_scale, currentPy + vpcy * v_scale); ctx.lineTo(currentPx + vpx * v_scale, currentPy + vpy * v_scale);
ctx.strokeStyle = 'rgba(173, 181, 189, 0.9)'; ctx.lineWidth = 2; ctx.stroke(); ctx.setLineDash([]);
drawArrow(currentPx, currentPy, currentPx + vpx * v_scale, currentPy + vpy * v_scale, '#198754', 5);
}
if (showAccel.checked) {
const a_scale = 0.6;
const ax = cx - currentPx;
const ay = cy - currentPy;
drawArrow(currentPx, currentPy, currentPx + ax * a_scale, currentPy + ay * a_scale, '#dc3545', 5);
}
}
function loop() {
if (isPlaying && !isDraggingP) theta += getDirection() * omega;
drawFrame();
requestAnimationFrame(loop);
}
resetToProblemState();
loop();
</script>
</body>
</html>