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126 lines
5.8 KiB
HTML
126 lines
5.8 KiB
HTML
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<h1 class="center">Centroid</h1>
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<p class="center"><b>And Center of Gravity</b></p>
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<p>The <b>Centroid</b> is the average position of all the points of an object.</p><p class="center"><img src="images/centroid.svg" alt="Centroid" /></p>
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<p>When we cut a plane shape from a piece of card it balances perfectly on its centroid.</p>
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<p><i>The geographic center of the USA was found this way (near Lebanon, Kansas) in 1918.</i></p>
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<h2>Center of Gravity</h2>
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<p>The <span class="center"><b>Center of Gravity</b></span> is the same as the centroid when the density is the same throughout.</p>
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<p><b>Center of gravity</b>, <b>center of mass</b> and <b>centroid</b> are all the same for simple solids.</p>
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<p>They are often marked by a <b>cross</b> or <b>dot</b> and sometimes the letters <b>CG</b> or just <b>G</b></p>
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<p class="center"><img src="images/torus-centroid.jpg" width="200" height="146" alt="torus centroid" /><br>
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For a <a href="torus.html">torus</a> the centroid is at the very center<br>
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(even though there is no part of the torus there!)</p>
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<p class="center"><img src="images/cone-centroid.jpg" width="185" height="197" alt="cone centroid" /><br>
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For a right solid <a href="cone.html">cone</a> the centroid is on<br>
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the center line and ¼ of the way from the base</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/car-centroid.jpg" width="309" height="104" alt="car centroid" /></p>
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<p>The center of gravity of a car can be very hard to figure out, as there is lots of empty space and materials of different density (such as the engine vs the seats).</p>
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<div style="clear:both"></div>
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<p>When doing calculations we can often <b>replace an object with its center of gravity</b>.</p>
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<div class="example">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../physics/images/hammer-drop.gif" width="150" height="341" alt="hammer drop rotates about centroid" /></p>
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<h3>Example: You drop a hammer!</h3>
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<p> </p>
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<p>It may spin a little, but its <b>center of gravity will fall straight down</b>.</p>
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<p> </p>
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<p>It also drops faster and faster due to gravity.</p>
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<p> </p>
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<p>(The only complication is air resistance, which affect its motion more as it goes faster.)</p>
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</div>
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<p>A force that goes <b>through the center of gravity</b> won't cause any rotation. In fact you can balance an object by supporting it directly below its center of gravity.</p>
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<p class="center"><img src="images/hammer-balance.gif" width="250" height="141" alt="hammer balance at centroid" /></p>
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<h2>Centroid of a Triangle</h2>
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<p>Where the medians intersect is the centroid. A median is a line segment from a corner to the midpoint of the opposite side.</p>
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<p>Try moving points A, B or C:</p>
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<iframe src="igeom-triangle-median.html" scrolling="no" style="width:362px; height:282px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
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<p> </p>
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<script>getQ(7480, 7484, 11959, 11961, 17567, 17566, 17570, 7485, 13478, 17564);</script> </div>
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