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| <h3 id="back-link"><a href="../#2.8">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../#2.8">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $2.8.37^*.$ 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. |
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| For problem $2.8.37^*$ | | For problem $2.8.37^*$ |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| <img src="2.8.37.jpg" | | <img src="2.8.37.jpg" |
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| Geometry of the problem | | Geometry of the problem |
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| <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 $\omega$ |
| $$\left\{\begin{matrix} | | $$\left\{\begin{matrix} |
| \frac{h}{R} = \frac{u}{v} \\ | | \frac{h}{R} = \frac{u}{v} \\ |
| u=\omega R | | u=\omega R |
| \end{matrix}\right.$$ | | \end{matrix}\right.$$ |
| From where | | From where |
| $$\boxed{\omega=\frac{hv}{R^2}}$$ | | $$\boxed{\omega=\frac{hv}{R^2}}$$ |
| </p> | | </p> |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $$\omega=\frac{hv}{R^2}$$ | | $$\omega=\frac{hv}{R^2}$$ |
| </p> | | </p> |
| <p style="text-align: right; font-style: italic; font-size: 14;"> | | <p style="text-align: right; font-style: italic; font-size: 14;"> |
| Yuldashev Ulugbek<br> | | Yuldashev Ulugbek<br> |
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