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294 lines
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Units in Equations</h1>
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<p>Here are some common <a href="../measure/metric-system.html">Units</a> in Physics:</p>
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<div class="simple">
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<table align="center" width="460px" border="0">
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<tbody>
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<tr>
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<th align="right" width="25">Property</th>
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<th align="right" width="25">Name</th>
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<th align="right" width="25">Symbol</th>
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</tr>
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<tr align="right">
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<td>Length</td>
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<td>meter</td>
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<td><b>m</b></td>
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</tr>
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<tr align="right">
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<td>Mass</td>
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<td>kilogram</td>
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<td><b>kg</b></td>
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</tr>
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<tr align="right">
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<td>Time</td>
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<td>second</td>
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<td><b>s</b></td>
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</tr>
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<tr align="right">
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr align="right">
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<td>Force</td>
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<td>Newton</td>
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<td><b>N</b></td>
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</tr>
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<tr align="right">
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<td>Energy</td>
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<td>Joule</td>
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<td><b>J</b></td>
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</tr>
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<tr align="right">
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<td>Per second</td>
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<td>Hertz</td>
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<td><b>Hz</b></td>
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</tr>
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</tbody></table>
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</div>
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<p>And we put <a href="../metric-numbers.html">Metric Number Prefixes</a> in front of the symbol to write larger or smaller values:</p>
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<table align="center" cellspacing="2" cellpadding="5" border="0">
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<tbody>
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<tr bgcolor="#FF99FF">
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<td align="center"><b>Name</b></td>
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<td align="center"><b>The
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Number</b></td>
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<td class="larger" align="center"><b>Prefix</b></td>
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<td align="center"><b>Symbol</b></td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">trillion</td>
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<td align="right">1,000,000,000,000</td>
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<td class="larger" align="center">tera</td>
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<td align="center">T</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">billion</td>
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<td align="right">1,000,000,000</td>
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<td class="larger" align="center">giga</td>
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<td align="center">G</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">million</td>
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<td align="right">1,000,000</td>
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<td class="larger" align="center">mega</td>
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<td align="center">M</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">thousand</td>
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<td align="right">1,000</td>
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<td class="larger" align="center">kilo</td>
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<td align="center">k</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">hundred</td>
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<td align="right">100</td>
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<td class="larger" align="center">hecto</td>
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<td align="center">h</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">ten</td>
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<td align="right">10</td>
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<td class="larger" align="center">deka</td>
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<td align="center">da</td>
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</tr>
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<tr align="center" bgcolor="#99CCFF">
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<td><b>unit</b></td>
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<td><b>1</b></td>
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<td class="larger" align="center"> </td>
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<td> </td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">tenth</td>
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<td>0.1</td>
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<td class="larger" align="center">deci</td>
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<td align="center">d</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">hundredth</td>
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<td>0.01</td>
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<td class="larger" align="center">centi</td>
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<td align="center">c</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">thousandth</td>
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<td>0.001</td>
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<td class="larger" align="center">milli</td>
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<td align="center">m</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">millionth</td>
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<td>0.000 001</td>
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<td class="larger" align="center">micro</td>
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<td align="center">µ</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">billionth</td>
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<td>0.000 000 001</td>
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<td class="larger" align="center">nano</td>
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<td align="center">n</td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td align="center">trillionth</td>
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<td>0.000 000 000 001</td>
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<td class="larger" align="center">pico</td>
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<td align="center">p</td>
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</tr>
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</tbody></table>
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<p>Examples:</p>
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<ul>
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<li><b>km</b>: <b>k</b> for kilo, <b>m</b> for meter becomes <b>kilometer</b> (a thousand meters)</li>
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<li><b>mm</b>: <b>m</b> for milli, <b>m</b> for meter becomes <b>millimeter</b> (a thousandth of a meter)</li>
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<li><b>MN</b>: <b>M</b> for mega, <b>N</b> for Newton becomes <b>meganewton</b> (a million Newtons)</li>
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<li><b>g</b>: <b>g</b> for gram, one symbol only is just the unit, so that is <b>grams</b></li>
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<li><b>µs</b>: µ for micro, <b>s</b> for second becomes <b>microsecond</b> (a millionth of a second)</li>
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</ul>
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<p>Now ... how do we us them in equations?</p>
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<p>First: it is common to just <b>use the symbol</b> (such as km for kilometers).</p>
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<h2>Adding and Subtracting</h2>
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<p>Use the <b>same units</b> when we add or subtract!</p>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../algebra/images/table.jpg" alt="table" height="111" width="200"></p>
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<h3>Example: Sam is designing a new table. The old table is 2 m long. The new table should be 200 mm longer:</h3>
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<p class="center larger">2 m + 200 mm = <b>?</b></p>
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<p>The units need to be the same!</p>
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<p>We can choose m (meters) or mm (millimeters).</p>
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<p>Let's choose mm. 1 m is 1000 mm, so:</p>
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<p class="center larger">2000 mm + 200 mm = 2200 mm</p>
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<p><b>Or</b> we could choose m:</p>
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<p class="center larger">2 m + 0.2 m = 2.2 m</p>
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</div>
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<h2>Multiplying and Dividing</h2>
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<p>When multiplying put the units next to each other</p>
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<p>When dividing put the unit after "<b>/</b>"</p>
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<p>Like this:</p>
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<div class="example">
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<h3>Example: Alex walks 100 m in 80 seconds, what average speed is that?</h3>
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<p>Speed is distance/time</p>
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<p class="center larger">Speed = <span class="intbl">
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<em>100 m</em>
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<strong>80 s</strong>
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</span>= 1.25 m/s</p>
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<p>100 divided by 80 is 1.25, and m divided by s is m/s</p>
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</div>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/ball-kick-2.jpg" alt="ball kick " height="190" width="200"></p>
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<h3>Example: Hunter kicks a soccer ball.
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It goes from 0 to 32 m/s in 0.1 seconds. What is the acceleration?</h3>
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<p><a href="../measure/metric-acceleration.html">Acceleration</a> is:</p>
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<p class="center large"><span class="intbl">
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<em>Change in Velocity (m/s)</em>
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<strong>Time (s)</strong>
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</span></p>
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<p>Put in the values we know:</p>
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<p class="center">Acceleration = <span class="intbl">
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<em>32 m/s − 0 m/s</em>
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<strong>0.1s</strong>
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</span>= 320 m/s<sup>2</sup></p>
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<p>The "m/s" becomes "m/s /s" which is m/<span class="center">s<sup>2</sup></span></p>
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</div>
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<p>Sometimes there is a special unit that is made up of other units:</p>
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<div class="example">
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<h3>Example: The soccer ball weighs 0.4 kg, what is the force of Hunter's kick?</h3>
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<p>We can use <a href="force.html">Newton's Second Law of Motion</a>:</p>
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<p class="center large"><b>F</b> = m<b>a</b></p>
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<p>The mass m = 0.4kg,<br>
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and we already calculated the acceleration: a = 320 m/s<sup>2</sup></p>
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<p class="center larger">F = 0.4 kg × 320 m/s<sup>2</sup></p>
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<p class="center larger">F = 128 kg m/s<sup>2</sup></p>
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<p>1 Newton (N) is the usual measure of force, and equals 1 kg m/s<sup>2</sup>, so:</p>
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<p class="center larger">F = 128 N</p>
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</div>
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<p> </p>
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<div class="related">
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<a href="../metric-numbers.html">Metric Number Prefixes</a>
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<a href="index.html">Physics Index</a>
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</div>
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