Consider a circular$-$motion problem in which tension not only must provide the proper radial acceleration but also must balance gravity. As we shall see, it can do both. A tetherball is attached to a swivel in the ceiling by a light cord of length LL$,$ as measured from the ceiling to the center of the tetherball. When the ball is hit by a paddle, it swings in a horizontal circle with constant speed vv$,$ and the cord makes a constant angle with the vertical direction. The ball goes through one revolution in time TT$.$ Assuming that TT$,$ mass mm$,$ and length LL of the rope are known, derive algebraic expressions for the tension FTFT in the cord and the angle $.$ What is the period TT of the ball$$s motion if L$=2\mathrm{.}5$mL$=2\mathrm{.}5$m and the cord makes an angle of $=20$$=20$ with the vertical?

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