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<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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<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> astrosander01@gmail.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="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
<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. ">
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
<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">
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<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
<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.
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> astrosander01@gmail.com <br></small>
<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>
