$1.5.2.$ 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?
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
$$\fbox{$v_\text{rope} = v_O = \omega \cdot (R - r)$}$$
$$v_\text{reel} = \omega R$$ $$v_\text{cargo} = \omega (R - r)$$