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  <h4>Statement</h4>
  <p>
    $5.2.9$
    A molecular projector creates a ribbon-shaped narrow beam of silver's atoms that arrive to internal surface of a cylinder of radius $R = 30$ cm and form a spot. The device rotates with angular velocity $\omega = 100\pi$ s$^{-1}$. Find the beam's velocity, if the spot deviates an angle $\varphi=0.314$ rad respect to initial position.
  </p>
  <center>
    <figure>
      <img src="statement.png"
        loading="lazy" alt="5.2.9" width="200" />
      <figcaption>
        For problem 5.2.9
      </figcaption>
    </figure>
  </center>
  <h4>Solution</h4>
   <p class="TxtSolutions">
    When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
    </p>
    <center>
        $\varphi=\omega t \\;(1)$
    </center>
    The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
    <center>
      $R=vt \\;(2)$
    </center>
    <p class="TxtSolutions">
        Dividing $(2)$ by $(1)$ and separating $v$
    </p>
    <center>
      $\boxed{v = \frac{\omega R}{\varphi}=300 \\;{\rm{m/s}}}$ 
    </center>
    <p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">   
        BSc. Luis Daniel Fernández Quintana<br>
        Physics Department (FCNE)<br>
        Universidad de Oriente, Cuba<br>
      </p>
</article>