{"id":58392,"date":"2026-01-05T04:44:29","date_gmt":"2026-01-04T19:44:29","guid":{"rendered":"https:\/\/phys-edu.net\/wp\/?p=58392"},"modified":"2026-01-05T04:44:29","modified_gmt":"2026-01-04T19:44:29","slug":"cant-see-it-in-the-textbook-a-circular-motion-tool-that-makes-velocity-and-acceleration-directions-instantly-clear","status":"publish","type":"post","link":"https:\/\/phys-edu.net\/wp\/?p=58392&lang=en","title":{"rendered":"Can\u2019t See It in the Textbook? A Circular Motion Tool That Makes Velocity and Acceleration Directions Instantly Clear"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #339966;\"><strong>I&#8217;m Ken Kuwako, your Science Trainer. To me, every day is an experiment.<\/strong><\/span><\/p>\n<p> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-31696 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2018\/06\/3b146492c3f39551c01b8868247d9a18.png\" alt=\"\" width=\"444\" height=\"331\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2018\/06\/3b146492c3f39551c01b8868247d9a18.png 934w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2018\/06\/3b146492c3f39551c01b8868247d9a18-300x224.png 300w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2018\/06\/3b146492c3f39551c01b8868247d9a18-768x572.png 768w\" sizes=\"auto, (max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Think about the spinning teacups at an amusement park, the moon drifting through the night sky, or even your clothes tumbling in the washing machine. Our world is absolutely full of <b>circular motion<\/b>\u2014things going round and round. However, as soon as we try to study this common movement in a physics classroom, it suddenly feels incredibly complicated, doesn&#8217;t it?<\/p>\n<p>Angular velocity, frequency, periods&#8230; trying to grasp the essence of such dynamic movement using only the static diagrams and equations in a textbook is a tough challenge. To bridge that gap, I\u2019ve developed a special teaching tool designed to unlock the mysteries of circular motion for students and teachers alike.<\/p>\n<h3>Why is Circular Motion So Hard to Teach?<\/h3>\n<p> When teaching &#8220;uniform circular motion,&#8221; the biggest hurdle for both teachers and students is <b>visualization<\/b>. Because the direction of travel is constantly changing, explaining the orientation of velocity and acceleration using only a chalkboard or verbal descriptions often leaves people feeling lost.<\/p>\n<p>To solve this, I created a simulation that is simple yet hits all the essential points. First, take a look at this video to see it in action:<\/p>\n<p><iframe loading=\"lazy\" title=\"\u6559\u5e2b\u7528Scratch\u6559\u6750\uff01\u7b49\u901f\u5186\u904b\u52d5\" width=\"1140\" height=\"855\" src=\"https:\/\/www.youtube.com\/embed\/2PInsu-quuM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<h3>A System for Intuitively Understanding Vectors<\/h3>\n<p> With this tool, you can observe a ball moving in a circle in real-time. The key feature isn&#8217;t just the rotation\u2014it&#8217;s the display of <b>two crucial arrows<\/b> that represent the physics at play.<\/p>\n<p>The <b>black arrow<\/b> represents the ball&#8217;s <b>velocity<\/b>, which always points along the tangent of the circle. Meanwhile, the <b>red arrow<\/b> represents <b>acceleration (centripetal force)<\/b>, which consistently points directly toward the center of the circle.<\/p>\n<p>One of the biggest &#8220;stumbling blocks&#8221; in physics is the question: &#8220;If the speed is constant, why is there acceleration?&#8221; By using this simulator, you can see for yourself that <b>because the direction is constantly changing, acceleration is occurring.<\/b> It makes the abstract concept visually undeniable.<\/p>\n<h3>Features Designed for the Classroom<\/h3>\n<p> I specifically kept the design minimal to ensure it\u2019s practical for actual lessons. Here are the main functions:<\/p>\n<p>\u30fb <b>Speed Toggle:<\/b> You can speed up the ball&#8217;s rotation with a single click. \u30fb <b>Pause\/Stop Button:<\/b> Use the button in the bottom left to freeze the action instantly.<\/p>\n<p>For example, when explaining <b>angular velocity (\u03c9)<\/b>, it is incredibly effective to stop the ball at a specific point and ask the students, &#8220;At this exact moment, which way is the ball trying to go?&#8221;<\/p>\n<h3>The Joy of Connecting the Scientific Dots<\/h3>\n<p> Mastering circular motion is a vital stepping stone toward understanding <b>simple harmonic motion<\/b> and the <b>universal gravitation<\/b> that governs the stars and planets. Seeing how an invisible &#8220;centripetal force&#8221; keeps an object tethered to its orbit helps us appreciate the hidden order of our universe.<\/p>\n<p>I hope you find this tool useful in your daily studies or classroom lessons. Next time, I\u2019m planning to take on the challenge of creating a tool for &#8220;simple harmonic motion,&#8221; which is closely related to this topic. Stay tuned!<\/p>\n<div class=\"g-ytsubscribe\" data-channelid=\"UCBoF1yPvFnXnSJ_Xe5AmXcw\" data-layout=\"full\" data-count=\"default\"><\/div>\n<h3>Inquiries and Requests<\/h3>\n<p> Let\u2019s make the wonders of science more accessible! I\u2019ve put together a collection of fun experiments you can try at home and tips on how to make them work. Feel free to explore!<\/p>\n<p>\u30fb My &#8220;Science Notebook&#8221; content is now a book! Details <a href=\"https:\/\/amzn.to\/42PMCEL\">here<\/a>. \u30fb Learn more about Ken Kuwako <a href=\"https:\/\/phys-edu.net\/wp\/?page_id=37\">here<\/a>. \u30fb For various requests (writing, lectures, science workshops, TV supervision\/appearances, etc.), click <a href=\"https:\/\/phys-edu.net\/wp\/?page_id=188\">here<\/a>. <span class=\"s2\">\u30fb Follow me on <a href=\"https:\/\/x.com\/kuwako\">X (Twitter)<\/a> for updates!<\/span><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/user\/kkuwako\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-35048\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2020\/03\/3d9640dad7bc5538e76f92da1966ee19.jpg\" alt=\"\" width=\"30\" height=\"21\" \/><\/a>Check out my experiment videos on the <a href=\"https:\/\/www.youtube.com\/user\/kkuwako?sub_confirmation=1\">Science Material Channel<\/a>!<\/p>\n<h3>\uff14\u6708\u306e\u30a4\u30c1\u30aa\u30b7\u5b9f\u9a13\uff01<\/h3>\r\n<ul>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?p=46937&amp;\">\u5149\u306e\u9b54\u6cd5CMY\u30a6\u30a9\u30fc\u30bf\u30fc\u30ad\u30e5\u30fc\u30d6<\/a>\uff1a\u5149\u306e\u9b54\u6cd5\u3092\u4f53\u9a13\u305b\u3088\uff01\u6c34\u3092\u6ce8\u3050\u3068\u65b0\u305f\u306a\u7acb\u65b9\u4f53\u304c\u51fa\u73fe\u3059\u308b\u9b54\u6cd5\u306e\u3088\u3046\u306a\u5b9f\u9a13\u3067\u3059\u3002<\/li>\r\n<\/ul>\r\n<img class=\"alignnone wp-image-47312 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c.jpg\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c.jpg 1292w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-272x300.jpg 272w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-928x1024.jpg 928w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/12\/71274840332ac4ee4620fb1475a1d79c-768x848.jpg 768w\" alt=\"\" width=\"267\" height=\"294\" \/>\r\n<h3 style=\"text-align: left;\"><span style=\"font-size: medium;\"><b><strong>\u30c6\u30ec\u30d3\u756a\u7d44\u30fb\u79d1\u5b66\u76e3\u4fee\u7b49\u306e\u304a\u77e5\u3089\u305b<\/strong><\/b><\/span><\/h3>\r\n<ul>\r\n \t<li>4\u67089\u65e5\uff08\u6728\uff09\u300cTHE\u7a81\u7834\u30d5\u30a1\u30a4\u30eb\u300d\uff08\u65e5\u672c\u30c6\u30ec\u30d3 \uff09\u306e\u79d1\u5b66\u76e3\u4fee\u3092\u884c\u3044\u307e\u3057\u305f\u3002\u591c7\u6642\u301c\u3068\u306a\u308a\u307e\u3059\u3002<\/li>\r\n<\/ul>\r\n<h3><span style=\"font-size: medium;\"><b>\u66f8\u7c4d<strong>\u306e\u304a\u77e5\u3089\u305b<\/strong><\/b><\/span><\/h3>\r\n<ul>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?p=61585\">\u30b5\u30af\u30bb\u30b915 \uff14\u6708\u53f7<\/a>\u306b\u3066\u3001\u91ce\u7403\u306e\u79d1\u5b66\u306b\u3064\u3044\u3066\u8a18\u4e8b\u3092\u57f7\u7b46\u3057\u307e\u3057\u305f\uff082026\/3\uff09<\/li>\r\n \t<li>\u300e\u5927\u4eba\u306e\u305f\u3081\u306e\u9ad8\u6821\u7269\u7406\u5fa9\u7fd2\u5e33\u300f\uff08\u8b1b\u8ac7\u793e\uff09\u2026\u4e00\u822c\u5411\u3051\u306b\u65e5\u5e38\u306e\u7269\u7406\u306b\u3064\u3044\u3066\u516c\u5f0f\u3092\u5143\u306b\u7d10\u89e3\u304d\u307e\u3057\u305f\u3002<a href=\"https:\/\/phys-edu.net\/wp\/?p=1827\">\u7279\u8a2d\u30b5\u30a4\u30c8<\/a>\u3067\u306f\u5b9f\u9a13\u3092\u591a\u6570\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<strong>\u203b\u5897\u5237\u304c\u304b\u304b\u308a\uff16\u5237\u3068\u306a\u308a\u307e\u3057\u305f\uff082026\/02\/01\uff09\r\n<img class=\"alignnone wp-image-10940 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0-300x262.jpg\" sizes=\"(max-width: 220px) 100vw, 220px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0-300x262.jpg 300w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2013\/12\/0811159a99f69eeff1a357e3daed84e0.jpg 311w\" alt=\"\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8 2014-07-05 0.43.51\" width=\"220\" height=\"192\" \/>\r\n<\/strong><\/li>\r\n \t<li>\u300e\u304d\u3081\u308b!\u5171\u901a\u30c6\u30b9\u30c8 \u7269\u7406\u57fa\u790e \u6539\u8a02\u7248\u300f\uff08\u5b66\u7814\uff09\u2026\u3000\u9ad8\u6821\u7269\u7406\u306e\u53c2\u8003\u66f8\u3067\u3059\u3002\u30a4\u30e9\u30b9\u30c8\u3092\u591a\u304f\u3057\u3066\u30a4\u30e1\u30fc\u30b8\u304c\u6301\u3066\u308b\u3088\u3046\u306b\u63cf\u304d\u307e\u3057\u305f\u3002\u6388\u696d\u306b\u3064\u3044\u3066\u3044\u3051\u306a\u3044\u3001\u7269\u7406\u304c\u82e6\u624b\u3001\u305d\u3093\u306a\u751f\u5f92\u306b\u304a\u3059\u3059\u3081\u3067\u3059\u3002<a href=\"https:\/\/phys-edu.net\/wp\/?p=45322\">\u7279\u8a2d\u30b5\u30a4\u30c8<\/a>\u306f\u3053\u3061\u3089\u3002\r\n<img class=\"alignnone wp-image-45718 aligncenter\" src=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c.jpg\" sizes=\"(max-width: 184px) 100vw, 184px\" srcset=\"https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c.jpg 756w, https:\/\/phys-edu.net\/wp\/wp-content\/uploads\/2024\/04\/dc1da64a8c8d1422062b4867c0607a1c-300x269.jpg 300w\" alt=\"\" width=\"184\" height=\"165\" \/><\/li>\r\n<\/ul>\r\n<h3><span style=\"font-size: medium;\"><b>\u8b1b\u5e2b\u30fb\u30b7\u30e7\u30fc\u30fb\u7814\u7a76\u7b49\u306e\u304a\u77e5\u3089\u305b<\/b><\/span><\/h3>\r\n<ul>\r\n \t<li>3\/20\uff08\u91d1\uff09\u3000\u65e5\u672c\u7406\u79d1\u6559\u80b2\u5b66\u4f1a\u30aa\u30f3\u30e9\u30a4\u30f3\u5168\u56fd\u5927\u4f1a2026\u300c<a href=\"https:\/\/phys-edu.net\/wp\/?p=60439\">\u6163\u6027\u306e\u6cd5\u5247\u306e\u6982\u5ff5\u5f62\u6210\u3092\u76ee\u6307\u3057\u305f\u63a2\u7a76\u7684\u306a\u5b66\u3073\u306e\u5b9f\u8df5\u300d<\/a>\u306b\u3064\u3044\u3066\u767a\u8868\u3057\u307e\u3057\u305f\u3002<\/li>\r\n \t<li>6\/14\uff08\u65e5\uff09\u3000\u5343\u8449\u5927\u5b66\u30a4\u30f3\u30b9\u30bf\u30ec\u30fc\u30b7\u30e7\u30f3\u300c\u63a2\u7a76\u300d\u306b\u3066\u8b1b\u5e2b\u3092\u52d9\u3081\u307e\u3059<\/li>\r\n \t<li>7\/18\uff08\u571f\uff09\u3000<a href=\"https:\/\/phys-edu.net\/wp\/?p=60018\">\u6559\u54e1\u5411\u3051\u5b9f\u9a13\u8b1b\u7fd2\u4f1a\u300c\u30ca\u30ea\u30ab\u30ab\u30b5\u30a4\u30a8\u30f3\u30b9\u30a2\u30ab\u30c7\u30df\u30fc\u300d\u306e\u8b1b\u5e2b\u3092\u3057\u307e\u3059<\/a>\u3002\u304a\u4f1a\u3044\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\r\n 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center;\">\uff0f<\/span><a style=\"text-align: center;\" href=\"https:\/\/www.threads.net\/@science_seeds?hl=ja\">Threads<\/a><\/li>\r\n<\/ul>\r\n<h3 style=\"text-align: center;\"><strong>Explore<\/strong><\/h3>\r\n<ul>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?page_id=30764\">\u697d\u3057\u3044\u5b9f\u9a13<\/a>\u2026\u304a\u5b50\u3055\u3093\u3068\u4e00\u7dd2\u306b\u5922\u4e2d\u306b\u306a\u308c\u308b\u30a4\u30c1\u30aa\u30b7\u306e\u79d1\u5b66\u5b9f\u9a13\u3092\u591a\u6570\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u9ad8\u6821\u7269\u7406\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u52d5\u753b\u6559\u6750\u3082\u7528\u610f\u3057\u307e\u3057\u305f\u3002<\/li>\r\n \t<li><a href=\"https:\/\/phys-edu.net\/wp\/?page_id=798\">\u7406\u79d1\u306e\u6559\u6750<\/a>\u2026 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