# Physics

A giant swing at a county fair consists of a vertical central shaft with a number of horizontal arms attahed at its upper end. Each arm supports a seat suspended from a 5.00 m long rod, the upper end of which is fastened to the arm at a point 3.00 m from the central shaft A. Find the time of one revolution of the swing if the rod is supporting the seat makes an angle of 30.0 degrees with the vertical. (b) does the angle depend on the weight of the passenger for a fiven rate of revolution.

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1. When the shaft is turning and the rod is at a 30 degree angle to vertical, the distance of the seat from the axis of rotation is
R = 3 + 5 sin 30 = 5.50 meters.
The angular rotation speed w (in radians/s) is given by
M R w^2 = T sin 30
where T is the tension in the rod. Vertical equilibrium tells you that
M g = T cos 30
Take the ratio of those two equations to cancel out T and you get
Rw^2/g = tan 30

From w you can get the period, P.

P = 2 pi/w

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