Edits to “Solution”, “Answer”

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−КТО СПИСЫВЕТ ТОТ ВРАГ АЛЛАХА
+$1.5.2.$ The angular velocity of the coil is $\omega$, the radius of the inner cylinder is $r$, and the radius of the outer cylinders is $R$. What are the velocities of the coil and load axis relative to the ground?
+
+![ For problem $1.5.2$ |483x353, 31%](../../img/1.5.2/statement.png)
+
+### Solution
+
+Consider the instantaneous axis of rotation passing through the point $O_1$, then the speed of the spool axis is
+
+$$
+\fbox{$v_\text{reel} = \omega R$}
+$$
+
+To find the speed of the load, consider the speed point $O$ as a superposition of the velocities of translational motion with the speed of the wheel center and the speed of rotation point $O$ relative to the wheel center.
+
+$$
+\vec{v_O} = \vec{v}_{in} + \vec{v}_{out}
+$$
+
+$$
+v_O = v_{out} – v_{in} = \omega R - \omega r = \omega\cdot (R - r)
+$$
+
+Any point of the thread, due to its inextensibility, has the same speed, therefore, the speed of the load
+
+$$
+\fbox{$v_\text{rope} = v_O = \omega\cdot (R - r)$}
+$$
+
+#### Answer