<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.

    <h3>Solution</h3>
    <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 $$\boxed{\omega=\frac{hv}{R^2}}$$

    <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>


<footer class="row container">
  <br>
    <p>
        <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
    </p>
    <p>
        <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
    </p>
</footer>