Let T= f(r) be a function of the Zhang Liwei r of the rope at the distance from the rotation axis r, because there is no tension at the end of the rope, so there is f(L)= 0. In this topic, the centripetal force required for the rotation of each short rope dr is provided by the tension difference f(r)- f(r+dr) between its two sides, and the rope is homogeneous. If the linear density is M/L, there is f (r).

F(r)- f(r+dr)= r*k*dr, df(r)= f(r+dr)- f(r), and the original formula can be changed to-DF (R)/DR = R * K.

Then f(r)= (-k*r*r/2)+ C can be obtained by indefinite integration, where c is a constant. And because f(L)= 0, it is substituted.

C=k*L*L/2, substitute W*W*M/L=k to get f (r) = (-w * w * m * r/2l)+(w * w * m * l/2).

Finally, substitute r=R and get the answer f(R)=(W*W*M*L/2)-(W*W*M*R*R/2L).

The tension in the problem exists between every two short pieces of rope and exists in pairs. The two Zhang Liwei interaction forces of each pair provide centripetal force for each short piece of rope.