<h3 id="back-link"><a href="/">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>

    <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>

    <h3>Solution</h3>
    <p>
      When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
      $$\varphi=\omega t \\;(1)$$
      The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
      $$R=vt \\;(2)$$
      Dividing $(2)$ by $(1)$ and separating $v$
      $$\boxed{v = \frac{\omega R}{\varphi}=300 \\;{\rm{m/s}}}$$ 
    </p>
    <p 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>


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