A ride in an amusement park consists of a cart which is supported by small wheel

Question

A ride in an amusement park consists of a cart which is supported by small wheels. Initially the cart is traveling in a circular path of radiusr (initial) = 14ftsuch that the angular rate of rotation istheta (dot) initial = 0.19rad/s.

If the attached cableOCis drawn inward at a constant speed of r (dot) = - 0.5ft/s, determine the tension it exerts on the cart at the instant r = 6ft. The cart and its passengers have a total weight of 380lb. Neglect the effects of friction. Hint:First show that the equation of motion in thethetadirection yields a

(theta direction) = r * theta (double dot) + 2r(dot)*theta(dot) = (1/r) * d[(r^2)theta(dot)]/dt = 0.When integrated, (r^2)theta(dot) = constant,where the constantis determined from the problem data.

Explanation / Answer

I am not sure about the hint, but we can conserve angular momentom and solve the problem.
Mr2 = 37.24M (initial...and is const

So at r = 6 ft ==> = 37.24M /62M = 1.034 rad/sec

The cart is moving inwards at const speed ==> Tension = Centrifugal force

==> tension = M2r = 2439.75 lb

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