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+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../#2.8">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $2.8.37^*.$ A wheel of radius $R$ can rotate freely around its axis. Drive belts moving at a speed $v$ are pressed against the side surface of the wheel at a distance $h$ from the axis of rotation. Determine the steady-state angular velocity of the wheel if its contact with the drive belt occurs only along the rim.
+
+</p>
+<center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" width="230" />
+ <figcaption>
+ For problem $2.8.37^*$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+
+</p>
+<center>
+ <figure>
+ <img src="2.8.37.jpg"
+ loading="lazy" width="300" />
+ <figcaption>
+ Geometry of the problem
+ </figcaption>
+ </figure>
+</center>
+<p>
+From the geometry of the problem
+$$\left\{\begin{matrix}
+\frac{h}{R} = \cos\alpha \\
+\frac{u}{v} = \cos\alpha
+\end{matrix}\right.$$
+Considering the relationship between velocity $u$ and angular velocity $\omega$
+$$\left\{\begin{matrix}
+\frac{h}{R} = \frac{u}{v} \\
+u=\omega R
+\end{matrix}\right.$$
+From where
+$$\boxed{\omega=\frac{hv}{R^2}}$$
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$\omega=\frac{hv}{R^2}$$
+ </p>
+ <p style="text-align: right; font-style: italic; font-size: 14;">
+ Yuldashev Ulugbek<br>
+ </p>
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