Merge pull request #810 from nature-of-code/notion-update-docs

one more chapter 3 layout tweak

content/03_oscillation.html

@@ -898,19 +898,19 @@ <h2 id="the-pendulum">The Pendulum</h2>
 </div>
 <p>Instead of using <em>linear</em> acceleration and velocity, I’m going to describe the motion of the pendulum in terms of <em>angular</em> acceleration and <em>angular </em>velocity, which refer to the change of the arm’s angle <span data-type="equation">\theta</span> relative to the pendulum’s resting position. I should first warn you, especially if you’re a seasoned physicist, that I’m going to conveniently ignore several important concepts here: conservation of energy, momentum, centripetal force, and more. This isn’t intended to be a comprehensive description of pendulum physics. My goal is to offer you an opportunity to practice your new skills in trigonometry and further explore the relationship between forces and angles through a concrete example.</p>
 <p>To calculate the pendulum’s angular acceleration, I’m going to use Newton’s second law of motion but with a little trigonometric twist. Take a look at Figure 3.19 and tilt your head so that the pendulum’s arm becomes the vertical axis. The force of gravity suddenly points askew, a little to the left—it’s at an angle with respect to your tilted head. If this is starting to hurt your neck, don’t worry. I’ll redraw the tilted figure and relabel the forces <span data-type="equation">F_g</span> for gravity and <span data-type="equation">T</span> for tension (Figure 3.20, left).</p>
+<p>Let’s now take the force of gravity and divide its vector into x- and y-components, with the arm as the new y-axis<em>.</em> These components form a right triangle, with the force of gravity as the hypotenuse (Figure 3.20, right). I’ll call them <span data-type="equation">F_{gx}</span> and <span data-type="equation">F_{gy}</span>, but what do these components mean? Well, the <span data-type="equation">F_{gy}</span> component represents the force that’s opposite to <span data-type="equation">T</span>, the tension force. Remember, the tension force is what keeps the bob from falling off.</p>
+<p>The other component, <span data-type="equation">F_{gx}</span>, is perpendicular to the arm of the pendulum, and it’s the force I’ve been looking for all along! It causes the pendulum to rotate. As the pendulum swings, the y-axis (the arm) will always be perpendicular to the direction of motion. Therefore, I can ignore the tension and <span data-type="equation">F_{gy}</span> forces and focus on <span data-type="equation">F_{gx}</span>, which is the <strong>net force</strong> in the direction of motion. And because this force is part of a right triangle, I can calculate it with . . . you guessed it, trigonometry!</p>
 <figure>
   <img src="images/03_oscillation/03_oscillation_17.png" alt="Figure 3.20: On the left, the pendulum is drawn rotated so that the arm is the y-axis. The right shows F_g zoomed in and divided into components F_{gx} and F_{gy}.">
   <figcaption>Figure 3.20: On the left, the pendulum is drawn rotated so that the arm is the y-axis. The right shows <span data-type="equation">F_g</span> zoomed in and divided into components <span data-type="equation">F_{gx}</span> and <span data-type="equation">F_{gy}</span>.</figcaption>
 </figure>
-<p>Let’s now take the force of gravity and divide its vector into x- and y-components, with the arm as the new y-axis<em>.</em> These components form a right triangle, with the force of gravity as the hypotenuse (Figure 3.20, right). I’ll call them <span data-type="equation">F_{gx}</span> and <span data-type="equation">F_{gy}</span>, but what do these components mean? Well, the <span data-type="equation">F_{gy}</span> component represents the force that’s opposite to <span data-type="equation">T</span>, the tension force. Remember, the tension force is what keeps the bob from falling off.</p>
-<p>The other component, <span data-type="equation">F_{gx}</span>, is perpendicular to the arm of the pendulum, and it’s the force I’ve been looking for all along! It causes the pendulum to rotate. As the pendulum swings, the y-axis (the arm) will always be perpendicular to the direction of motion. Therefore, I can ignore the tension and <span data-type="equation">F_{gy}</span> forces and focus on <span data-type="equation">F_{gx}</span>, which is the <strong>net force</strong> in the direction of motion. And because this force is part of a right triangle, I can calculate it with . . . you guessed it, trigonometry!</p>
+<p>The key here is that the top angle of the right triangle is the same as the angle <span data-type="equation">\theta</span> between the pendulum’s arm and its resting position. Just as I demonstrated in the discussion of polar coordinates, the sine and cosine functions allow me to separate out the components of the gravity force (the hypotenuse) according to this angle. For <span data-type="equation">F_{gx}</span>, I need to use sine:</p>
 <div class="half-width-right">
   <figure>
     <img src="images/03_oscillation/03_oscillation_18.png" alt="Figure 3.21: F_{gx} is now labeled F_p, the net force in the direction of motion.">
     <figcaption>Figure 3.21: <span data-type="equation">F_{gx}</span> is now labeled <span data-type="equation">F_p</span>, the net force in the direction of motion.</figcaption>
   </figure>
 </div>
-<p>The key here is that the top angle of the right triangle is the same as the angle <span data-type="equation">\theta</span> between the pendulum’s arm and its resting position. Just as I demonstrated in the discussion of polar coordinates, the sine and cosine functions allow me to separate out the components of the gravity force (the hypotenuse) according to this angle. For <span data-type="equation">F_{gx}</span>, I need to use sine:</p>
 <div data-type="equation">\sin(\theta) = F_{gx} / F_g</div>
 <p>Solving for <span data-type="equation">F_{gx}</span>, I get this:</p>
 <div data-type="equation">F_{gx} = F_g \times \sin(\theta)</div>