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<meta name="description" content="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.">
<meta property="og:title" content="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.">
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<meta property="og:description" content="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.">
<title>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.</title>
$2.8.37^*.$ 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.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem $2.8.37^*$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="2.8.37.jpg"
loading="lazy" width="300" />
<figcaption>
Geometry of the problem
</figcaption>
</figure>
</center>
<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 $\omega$
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<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 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.">
<meta name="description" content="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.">
<meta property="og:title" content="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.">
<meta property="og:title" content="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.">
<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 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.">
<meta property="og:description" content="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.">
<title>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.</title>
<title>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.</title>
$2.8.37^*.$ 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.
$2.8.37^*.$ 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.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $2.8.37^*$
For problem $2.8.37^*$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.8.37.jpg"
<img src="2.8.37.jpg"
loading="lazy" width="300" />
loading="lazy" width="300" />
<figcaption>
<figcaption>
Geometry of the problem
Geometry of the problem
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
From the geometry of the problem
From the geometry of the problem
$$\left\{\begin{matrix}
$$\left\{\begin{matrix}
\frac{h}{R} = \cos\alpha \\
\frac{h}{R} = \cos\alpha \\
\frac{u}{v} = \cos\alpha
\frac{u}{v} = \cos\alpha
\end{matrix}\right.$$
\end{matrix}\right.$$
Considering the relationship between velocity $u$ and angular velocity $\omega$
Considering the relationship between velocity $u$ and angular velocity $\omega$
<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>
