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centripetal-acceleration.html
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<!DOCTYPE html>
<html lang="en">
<head>
<title>NBPSP - Centripetal Acceleration</title>
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<meta name="description" content="The New Buffalo Physics Skatepark's official website, with lots to learn about science, math, and fun.">
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<meta name="author" content="Wesley McGinn">
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<h2><abbr title="New Buffalo Physics Skatepark">NBPSP</abbr></h2>
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<li class="ham" onclick="location.assign('./friction.html')">Friction</li>
<li class="ham" onclick="location.assign('./force-normal.html')">Force Normal</li>
<li class="ham" onclick="location.assign('./centripetal-acceleration.html')">Centripetal Acceleration</li>
<li class="ham" onclick="location.assign('./momentum.html')">Momentum</li>
<li class="ham" onclick="location.assign('./potential-to-kinetic-energy.html')">Potential to Kinetic Energy</li>
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<div class="col" id="col1">
<section>
<h1 class="blue">Centripetal Acceleration</h1>
<article>
<p>When an object is going around a curve, centripetal acceleration is what pulls that object towards the center of the circular path it is traveling in, allowing that object to turn rather than traveling in a straight line.</p>
<p>This can sometimes be a tricky concept to understand. After all, if you are in a vehicle driving around in a circle at a constant speed of 20<abbr title="Miles per hour">mph</abbr>, how can you be accelerating? You're not speeding up or slowing down.</p>
<p>True, your speed isn't changing. But if you're not accelerating towards a point, your vehicle will simply travel in a straight line.</p>
<p>Take a look at the diagram below:</p>
<img class="demo" type="image/svg+xml" src="./images/sketches/centripetalCar.svg" alt="Diagram showing car driving around curve, with arrow pointing from car to center of circular path, representing the direction of centripetal acceleration, and an arrow pointing in the direction the car is facing, representing the current direction of travel">
<p>Notice the blue arrow, labeled <i>"Direction of Movement"</i>. If the car wasn't accelerating in a specific direction, it would simply follow the direction of this arrow. However, due to the friction between the road and the tires of the car, the car is being accelerated towards the point labeled <i>"Center of Circular Path"</i>.</p>
<p>The car is getting farther away from this point simply because of its direction of movement, but it is also being accelerated, with centripetal acceleration, towards it. These two things happening at the same time cancel each other out in a delicate balance, keeping the car the same distance away from the point while still technically accelerating towards it.</p>
<p>This is why you are pushed to one side of your car when you go around a sharp bend. Centripetal acceleration is accelerating the vehicle to your right or to your left, depending on which direction you are turning in. So, in the same way you may be pressed against the back of your seat when you accelerate quickly forward, you are pressed against your left door when you make a right turn.</p>
</article>
</section>
<section>
<h1 class="orange">How Does This Apply to Skateboarding?</h1>
<article>
<p>When you turn right on your skateboard, you have to lean right to turn right, and when you turn left, you have to lean left. This is because centripetal acceleration is accelerating your skateboard in one direction, and you need to accelerate with the skateboard or you will fall off. (You probably already know this from experience.) The same concept of leaning in the direction you turn goes for scooters, bicycles, longboards, motorcycles, and more, all because of centripetal acceleration.</p>
</article>
</section>
<section>
<h1>What Determines Centripetal Acceleration?</h1>
<article>
<p>Centripetal Acceleration is determined by the following formula, where <var>a</var> is your centripetal acceleration, <var>v</var> is your velocity, and <var>r</var> is the radius of your turn (the distance between you and the center of the circular path you are traveling in):</p>
<div class="equation"><var title="Centripetal acceleration (in meters per second per second)">a</var> = <var title="Velocity (in meters per second)">v</var><sup>2</sup> / <var title="Radius of turn (in meters)">r</var></div>
<p>You can easily use this formula to determine your centripetal acceleration by simply entering some data in the Centripetal Acceleration Calculator on this page.</p>
</article>
</section>
</div>
<div class="col" id="col2">
<section>
<h1>Centripetal Acceleration Calculator</h1>
<fieldset>
<legend>Find your centripetal acceleration:</legend>
<label for="centripetal_velocity">Velocity:</lablel>
<input id="centripetal_velocity" type="number" value="5.47" min="0" max="100000000" oninput="centripetalCalculator.calculate()"/>
<label for="centripetal_velocity"><b><abbr title="Meters per second">m/s</abbr></b></label><br><br>
<label for="centripetal_radius">Turn Radius:</lablel>
<input id="centripetal_radius" type="number" value="10" min="0" max="100000000" oninput="centripetalCalculator.calculate()"/>
<label for="centripetal_radius"><b><abbr title="Meters">m</abbr></b></label><br><br>
<label for="centripetal_out">Centripetal Acceleration:</label><br>
<div class="output" id="centripetal_out">2.99 <abbr title="Meters per second per second">m/s<sup>2</sup></abbr></div>
</fieldset>
</section>
<section>
<h1>How To Know Your Velocity</h1>
<article>
<p>You probably used a QR code to get to this page. If you are rolling down the ramp that this QR code is on top of, your final velocity will be 4.89 <abbr title="Meters per second">m/s</abbr>. To learn more about where this value comes from, see the <a href="./potential-to-kinetic-energy.html">Potential to Kinetic Energy Page</a> while knowing that this ramp is four feet tall. You can also use the calculator on that page to know your velocity coming down from any skatepark element, as long as you know the height.</p>
</article>
</section>
<section>
<h1>How To Know Your Turn Radius</h1>
<article>
<p>You will notice that there are curved markings of different sizes near the bottom of one side of the ramp. These curves are turn radius measurements that you can use to approximate your turn radius. For example, if you turn along a curve marked "4m", your turn radius is about four meters. You can then enter the number 4 into the "turn radius" blank in the calculator above and, if the entered velocity is correct, know the value of your centripetal acceleration!</p>
</article>
</section>
</div>
<div class="col" id="col3">
<section>
<h1>About This Element</h1>
<article>
<p>The QR code you may have used to access this page is found on top of a two-way ramp, one side leading into a halfpipe and the other leading down a ramp with a bank (flat transition) toward radius marks on the ground that will allow you to know your turn radius.</p>
<p>The ramp is four feet high, so you will be coming off with an approximate velocity of 4.89 <abbr title="Meters per second">m/s</abbr>.</p>
<img class="demo" type="image/svg+xml" src="./images/sketches/twoWayRamp.svg?v=1" alt="Graphic of person rolling down a bank ramp, with a transition ramp on the other side.">
</article>
</section>
<section>
<h1 class="noticable red">CHALLENGE!</h1>
<article>
<p>This challenge is perhaps the <i>most dangerous</i> of all the skatepark challenges. That is why, should you dare to accept the challenge, you are obligated to <b class="red">NOT GET HURT</b> in your attempts to succeed.</p>
<p>Your goal is to experience as much centripetal acceleration as possible on flat ground. The radius marks on the ground can help with this, as can the fact that your velocity will be 4.89 <abbr title="Meters per second">m/s</abbr> after going down the ramp.</p>
<p>You will get to understand and experience the power of centripetal acceleration as you try to make the sharpest turn possible at the highest speed. You can compete with friends or with yourself, trying to break your previous record. Again, however, make sure you <b class="red">DON'T GET HURT</b> while trying to do this!</p>
<p>Good Luck!</p>
</article>
</section>
<section>
<h1 class="green">What's Next?</h1>
<p>Ready to experience <i>even more</i> centripetal acceleration? Make <b>sharper turns</b> at <b>higher speeds</b> with the help of <b><i>FORCE NORMAL</i>....</b></p>
<a href="./force-normal.html"><button>Go to Force Normal Page</button></a>
</section>
</div>
</div>
</body>
<script src="./scripts/skateboard.js?v=1" type="text/javascript"></script>
<script src="./scripts/calculators.js?v=2" type="text/javascript"></script>
<script type="text/javascript">
centripetalCalculator.setup();
</script>
</html>