<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="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. ">
<meta property="og:title" content="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. ">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="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. ">
<title>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. </title>
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 $v$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="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. ">
<meta name="description" content="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. ">
<meta property="og:title" content="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. ">
<meta property="og:title" content="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. ">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="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. ">
<meta property="og:description" content="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. ">
<title>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. </title>
<title>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. </title>
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.
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>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" alt="5.2.9" width="200" />
loading="lazy" alt="5.2.9" width="200" />
<figcaption>
<figcaption>
For problem 5.2.9
For problem 5.2.9
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
$$\varphi=\omega t \;(1)$$
$$\varphi=\omega t \;(1)$$
The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
