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<h2 class="hd hd-2 unit-title">Intro to Uniform Circular Motion </h2>
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<p> Before looking at acceleration in general, we look at the special case of uniform circular motion where \(d\theta/dt=\text{constant}\). </p><p> As you go through the lesson, you will find this list of reading from the textbook complementary to the videos and exercises, and on many occasions these readings will contain relevant material to the presentation:</p><ul><li> Tangential and Radial Acceleration: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/6/6"><i class="it">chapter 6, section 3</i></a></li><li> Period and Frequency of Uniform Circular Motion: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/6/8"><i class="it">chapter 6, section 4</i></a></li></ul>
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<h2 class="hd hd-2 unit-title">L9v1: Uniform Circular Motion </h2>
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<p> Uniform Circular Motion: \(\frac{d\theta}{dt}=constant\)</p><p> The tangential component of the acceleration is zero.</p><p> The magnitude of the radial acceleration can be written as \(|a_r|=\frac{v^2}{r}=r \omega^2=r(2 \pi f)^2=\frac{4 \pi^2 r}{T^2}\).</p>
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<h3 class="hd hd-2">L9v1: Uniform Circular Motion </h3>
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<h2 class="hd hd-2 unit-title">L9v2: Uniform Circular Motion - Direction of the Acceleration</h2>
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<h2 class="hd hd-2 unit-title">L9Q1: Uniform Circular Motion - Magnitude of the Acceleration</h2>
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L9Q1: Uniform Circular Motion - Magnitude of the Acceleration
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Object A sits at the outer edge of a rotating disc, while object B sits halfway between the edge and the axis of rotation. The disc rotates with a constant angular velocity. The magnitude of the acceleration of Object B is: </p>
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<text> half the magnitude of the acceleration of Object A.</text>
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<text> the same as the magnitude of the acceleration of Object A.</text>
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<text> twice the magnitude of the acceleration of Object A.</text>
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<h2 class="hd hd-2 unit-title">L9Q2: Uniform Circular Motion - Magnitude and Direction of the Acceleration</h2>
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L9Q2: Uniform Circular Motion - Magnitude and Direction of the Acceleration
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<p> The diagram above shows the top view of a \(2.0 \textrm{kg}\) model train moving at a constant speed of
\(6.0 \textrm{ m/s}\) along a track made of circular sections of different radius connected by a straight section.
</p>
<table>
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<p>What is the magnitude and direction of the train's acceleration at Point <b>A</b>?</p>
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<p>What is the magnitude and direction of the train's acceleration at Point <b>C</b>?</p>
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<span class="trailing_text" id="trailing_text_lore_ls03_20133_9072a74cb54a4b5fb411fbb020da7047_2_1">m/s&#178;</span>
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<span class="trailing_text" id="trailing_text_lore_ls03_20133_9072a74cb54a4b5fb411fbb020da7047_4_1">m/s&#178;</span>
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<p>What is the magnitude and direction of the train&#8217;s acceleration at Point <b>B</b>?</p>
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<p>What is the magnitude and direction of the train&#8217;s acceleration at Point <b>D</b>?</p>
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<p> Period, \(T\), is defined as the amount of time it takes to go around once - the time to cover an angle of \(2\pi\) radians. </p><p> Frequency, \(f\), is defined as the rate of rotation, or the number of rotations in some unit of time.</p><p> Angular frequency, \(\omega\), is the rotation rate measured in radians.</p><p> These three quantities are related by \(f=\frac{1}{T}=\frac{\omega}{2\pi}\).</p><p> The speed at which an object goes around a circle can be related to these quantities through \(v=R \omega=\frac{2\pi R}{T}\).</p>
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<h2 class="hd hd-2 unit-title">L9Q3: Period and Frequency</h2>
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L9Q3: Period and Frequency
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The movie shows a large green ball moving on the outer circle and a small red ball on the inner circle. Both are moving with uniform circular motion. The radius of the green ball's circular path is 1.5 times the radius of the red ball's path. Carefully watch the video as many times as you need to answer the following questions. </p>
<p><b class="bfseries">(Part a)</b> What is [mathjaxinline]T_{red}/T_{green}[/mathjaxinline], the ratio of their periods? <p style="display:inline">[mathjaxinline]T_{red}/T_{green} =[/mathjaxinline] </p> <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls03_ls03_28_2_1" class=" capa_inputtype inline textline">
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<p><b class="bfseries">(Part b)</b> What is [mathjaxinline]\omega _{red}/\omega _{green}[/mathjaxinline], the ratio of their angular speeds? </p>
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<p style="display:inline">[mathjaxinline]\omega _{red}/\omega _{green} =[/mathjaxinline] </p>
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<p><b class="bfseries">(Part c)</b> What is [mathjaxinline]v_{red}/v_{green}[/mathjaxinline], the ratio of their speeds? <p style="display:inline">[mathjaxinline]v_{red}/v_{green} =[/mathjaxinline] </p> <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ls_ls03_ls03_28_4_1" class=" capa_inputtype inline textline">
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