Updated spacing between @ latex expressions

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revision #10424 parent #10017 GitHub c702ebe ← older newer →
en/1.5.18.md +8 −8
@@ -6,14 +6,14 @@
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<meta http-equiv="content-language" content="en">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
− <meta name="description" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega. There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
+ <meta name="description" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega . There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
<meta name="author" content="Aliaksandr Melnichenka">
<meta name="date" content="2023-10" scheme="YYYY-MM">
− <meta property="og:title" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega. There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
+ <meta property="og:title" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega . There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
<meta property="og:image" content="img/logo.png">
− <meta property="og:description" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega. There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
+ <meta property="og:description" content="The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega . There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.">
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− <title>The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega. There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.</title>
+ <title>The rod, with one end pivotally fixed on a horizontal plane, lies on the cylinder. Angular velocity of the rod \omega . There is no slippage between the cylinder and the plane. Find the dependence of the angular velocity of the cylinder on the angle \alpha between the rod and the plane.</title>
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@@ -84,23 +84,23 @@
</p>
<p>I share both honors with $dt$</p>
<p>
−$$ \frac{dx}{dt} = \frac{d\left(\frac{R}{\tan \alpha/2}\right)}{dt} $$
+$$ \frac{dx}{dt} = \frac{d\left(\frac{R}{\tan\alpha /2}\right)}{dt} $$
</p>
<p>Considering that $\omega = \frac{d \alpha}{dt}$ and $v = \frac{dx}{dt}$</p>
<p>
−$$ v = \frac{\omega R}{2 \sin ^2 \left(\frac{\alpha}{2}\right)} $$
+$$ v = \frac{\omega R}{2 \sin^2 \left(\frac{\alpha}{2}\right)} $$
</p>
<p>Let's write down the condition of no slippage</p>
<p>
$$ \omega ' R = v $$
</p>
<p>From here</p>
<p>
−$$ \fbox{$\omega ' = \frac{\omega}{2 \sin ^2 \left(\frac{\alpha}{2}\right)}$} $$
+$$ \fbox{$\omega ' = \frac{\omega}{2 \sin^2 \left(\frac{\alpha}{2}\right)}$} $$
</p>
</p>
− <h4>Answer: $\omega _0 = \omega /2 \sin^2 (\alpha /2)$</h4>
+ <h4>Answer: $\omega_0 = \omega /2 \sin^2 (\alpha /2)$</h4>
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unchanged lines 11