🎡 匀速圆周运动：速度大小不变、方向一直在变🎡 Uniform Circular Motion: Same Speed, Ever-Changing Direction
上一片里，摩擦力让冰壶慢慢停下——力能改变快慢。小火箭却在游乐园发现：还有的运动，快慢不变，方向却一刻不停。Last leaf, friction slowed the curling stone down — force can change how fast things go. But at the playground, the little rocket found a motion whose speed never changes while its direction never stops turning.
第 1 步：速度的方向，沿着圆的切线Step 1: Velocity points along the tangent
先看游乐园的转盘：小球转得稳稳的，速度箭头却一直在转。Start at the merry-go-round: the ball spins steadily, yet the velocity arrow keeps sweeping around.
速度不只有大小，还有方向。小球坐在匀速转动的转盘边缘，快慢始终不变，但速度方向一直沿着圆的切线（和半径垂直）。球转到哪里，箭头就指向哪里——“匀速”说的只是快慢，方向可一刻都没停过。Velocity has both size and direction. On a steadily turning merry-go-round the ball's speed never changes, yet its velocity keeps pointing along the tangent (perpendicular to the radius). Wherever the ball goes, the arrow follows — “uniform” only describes the speed, never the direction.
方向变了，速度变了吗？If the direction changes, has the velocity changed?
第 2 步：“匀速”其实在加速Step 2: “Uniform” is still accelerating
速度 = 快慢 + 方向：方向一变，速度就在变；速度在变，就有加速度。摩天轮匀速转动时，只改方向、不改大小，这个加速度恰好指向圆心，叫“向心加速度”。它和上一片的加速度是同一个概念，只是这次专门负责拐弯。Velocity = speed + direction. Change the direction and the velocity changes; a changing velocity means acceleration. When the Ferris wheel turns uniformly, only the direction changes — and that acceleration points straight to the center: centripetal acceleration. Same idea as the last leaf, now specialised for turning.
那转一圈要多久、转得多快，怎么描述？So how do we describe how long a lap takes, or how fast it goes?
第 3 步：转圈的快慢怎么算Step 3: Measuring the turning
转一圈用的时间叫周期 T；每秒转的圈数叫频率。小球每秒走过的弧长叫线速度，它等于圆周长 ÷ 周期：v = 2πr ÷ T。卫星绕地球一圈约 90 分钟，半径大，线速度接近 8 km/s——比子弹还快好几倍。The time for one lap is the period T; laps per second is the frequency. The arc covered each second is the linear speed, equal to the circumference ÷ period: v = 2πr ÷ T. A satellite laps the Earth in about 90 minutes — a huge radius gives it a linear speed near 8 km/s, several times faster than a bullet.
🎮 你来转一转（30 秒）🎮 Your turn to spin (30 seconds)
道理讲完了。拖转速滑块，盯着小球的速度箭头；再完成 4 个观察任务。Theory done. Drag the spin slider and watch the velocity arrow; then finish the 4 observation tasks.
一句话记住它：匀速圆周运动 = 快慢不变、方向时刻在变的运动——所以它一直在加速，加速度指向圆心。Remember it in one line: uniform circular motion = steady speed with a direction that never stops turning — so it is always accelerating, toward the center.
速度方向沿圆的切线、时刻在变；不变的只是快慢Velocity points along the tangent and keeps changing direction; only the speed stays steady速度一变就有加速度，它的方向指向圆心（向心加速度）A changing velocity means acceleration, pointing to the center (centripetal acceleration)周期 T = 转一圈的时间；线速度 v = 2πr ÷ TPeriod T = time for one lap; linear speed v = 2πr ÷ T
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
Back to tree
