Added 2.7.19

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+ <h3 id="back-link"><a href="../../#2.7">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $2.7.19^*.$ A uniform heavy rope, the ends of which are fixed on the same vertical, covers
+a weightless hoop. How fast does the hoop fall when released?
+</p>
+<center>
+ <figure>
+ <img src="2.7.19.png"
+ loading="lazy" width="160" />
+ <figcaption>
+ For problem $2.7.19^*$
+ </figcaption>
+ </figure>
+</center>
+<p>
+
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+
+</p>
+<center>
+ <figure>
+ <img src="2.7.19_1.png"
+ loading="lazy" width="200" />
+ <figcaption>
+Rotation of the hoop
+ </figcaption>
+ </figure>
+</center>
+<p>
+
+Hoof's moment of inertia
+$$I_0=mR^2$$
+Parallel axis theorem for point $A$
+$$I_A=2mR^2$$
+We express the external gravity moment $mg$, through the moment of inertia and angular acceleration
+$$I_A\cdot\varepsilon=mgR\Leftrightarrow 2mR^2\cdot\varepsilon=mgR\quad(1)$$
+When there is no slippage
+$$a = \varepsilon R$$
+Then, the $(1)$ expression could be rewritten as
+$$2a = g\Rightarrow\boxed{a=\frac{1}{2}g}$$
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$a=g/2$$
+ </p>
+ <p style="text-align: right; font-style: italic; font-size: 14;">
+ Almaskhan Arsen<br>
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