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class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Circular motion <a href="#" class="mark-page-favorite pull-right" data-pid="264" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../443/circular-motion-and-gravity.html">Circular motion and gravity</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Circular motion</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../circular-motion/1-laundry-sm-1.jpg" style="float: left; width: 250px; height: 167px;">We have all experienced circular motion. Here are some common thoughts among students...</p> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz"> If your speed is constant how can you be accelerating?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Velocity is a vector quantity. Anything travelling in a circular path is changing direction and, therefore, accelerating. A resultant force is required.</section> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz"> When you move in a circle it feels like you are being thrown out. So how do you stay in your seat?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">The forces in circular motion act towards the centre of the circle. The sensation of being 'flung outwards' comes from your inertia relative to the system.</section> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz"> If too many people join me on a roller coaster will we all fall to our death on the loop the loop?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">This would affect the total mass of the body, which in turn affects the kinetic energy required to make it round. Take a look at the following pages to find out!</section> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>Rather than considering displacement, velocity and time, in this topic we will consider the angular equivalents. It is helpful to recall that circular motion is <em>periodic</em>, which means it repeats in cycles.</p> <h4 style="text-align: center;"><img alt="" src="../../../ib/physics/activities/cm1.png" style="width: 257px; height: 233px;"></h4> <p style="text-align: center;"><strong>Time period (T)</strong> = time for one complete circle. Unit: s</p> <p style="text-align: center;"><strong>Frequency (f) </strong>= number of complete circles per second (<span class="math-tex">\(1\over T\)</span>). Unit: Hz (s<sup>-1</sup>)</p> <p style="text-align: center;"><strong>Angular displacement (θ)</strong> = angle swept out in radians. Unit: rad</p> <p style="text-align: center;"><strong>Angular velocity (ω)</strong> = angle swept out per unit time. Unit: rad s<sup>-1</sup> </p> <p>This could be a good time to revisit <a href="../267/radians.html" title="Radians">Radians</a>.</p> <p>Small angle approximation: Angle in radians = arc length/radius (<span class="math-tex">\(s \over r\)</span>). However, if the angle is small this is approximately the same as the chord length/radius.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <p><strong>Speed</strong> (distance / time) is related to the angular velocity.</p> <p style="text-align: center;"><span class="math-tex">\(v={2\pi r \over T}=\omega r\)</span></p> <p>Note that the units are now satisfactory (it's ok to ignore radians).</p> <p>The <strong>centripetal force</strong> is the <em>resultant force </em>acting towards the centre that makes a body travel in a circle.</p> <p style="text-align: center;"><span class="math-tex">\(F=m \omega^2 r={mv^2 \over r}\)</span></p> <p><img class="sibico" src="../../../img/sibico/exam-style.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Exam-style question"> Note that, if you are asked to name the force that is acting on an object, it will not be the 'centripetal force'. This is simply the consequence of the combination of the other forces at play.</p> <p>In everyday speech, we might refer to a 'centrifugal force' as flinging objects outward. In fact, this does not exist and instead is an effect of the absence of sufficient force while the system turns the corner. Relative motion does not always require a force on both objects.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1" data-mode="Normal" data-topics="517" data-subject-id="6" data-n-flashcards="6" style="text-align:center">Show flashcards</a></div><hr> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p><em>Check out this πg physics summary.</em></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388981800"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="264"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Circular motion</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/264/circular-motion"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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