i want to ask about the relation highlighted in yellow in the picture the equation of motion of this system can be obtained using the Lagrange formalism, but my question is about this relation i have had some issues in finding it i used fundamental relation of dynamics but i didn't find any result like that. the translation of the text in the image:
in the system of figure 11, the two pulleys we neglect the weight both have the same radius R. find the expressions of the kinetic energy, the potential energy and the equation of motion and the natural frequency of the oscillation. U is the potential energy. T is the kinetic energy.
thanks in advance.