The giant swing at a country fair consists of a vertical central shaft with a nu

Question

The giant swing at a country fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from 5.00 m long rod, the upper end of which is fastened to the arm at a point 3.00 cm from the central shaft. Find the time of one revolution of the swing if the rod supporting the seat makes an angle of 30 degrees with the vertical. This question has been answered before on Chegg, however I do not understand the thinking behind the math. I am trying to understand how to think in a different way. Please offer both a math and verbal explanation.

Explanation / Answer

Radius,r = 5 sin30 + 3.00m = 5.5 m The centripetal force is actually caused by the horizontal tension in the 5.00m cable. Centripetal force,F = T sin 30 (mv^2) / r = T sin 30 -------------(1) where, m = mass of person + seat v = tangential velocity r = radius The weight of the person and seat are balanced by the vertical tension in the 5.00m cable. mg = T cos 30 ----------------(2) Combine both equation (1) / (2), tan 30 = v^2 / rg v^2 = rg tan30 = 31.12 v = 5.57846m/s v = rW , where W is the angular velocity 5.57846 = (5.5)(W) W = 1.0143 rad/s 2(pi)(f) = W, where f is the frequency f = 0.16143 1/T = f , where T is the period. T = 1/f = 6.2s

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