You are at the carnival and decide to go on the swing ride. It is a high rotatin

Question

You are at the carnival and decide to go on the swing ride. It is a high rotating platform from which swing seats hang like pendulums. As the platform begins to turn, your swing's chain does not stay perpendicular to the ground but angles out from the vertical. If your distance from the center of rotation is 8.50 meters and you go around once every 12.0 seconds, what angle does your swing make with the vertical?

Explanation / Answer

It makes a maximum angle when it is horizontal with the center of rotation. Two forces act on the suspending body at that time. (i) Its weight, mg, downwards and (ii) tension, T, in the suspending rod upwards at the maximum angle ? with the vertical Balancing forces in the vertical and horizontal directions, Tcos? = mg and Tsin? = mv^2/r => tan? = v^2/rg = (2pr/T)^2 / rg => tan? = (4p^2r)/T^2g = (4p^2*8.5)/[(12)^2*9.8] => tan? = 0.2382 => ? = 13.4°

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