FYKOS Year 27 Series 5 Problem 5 — Babysitting · FYKOS 27 #27.5.5

Physics · mechanics

Problem

Consider a swing held up by two ropes of length

l=1.5\;\mathrm{m}

that hang from a pole of radius

r=4\;\mathrm{cm}

. The child sitting on the swing shall gain in the bottom dead center such a speed

v_{0}

that the child shall accomplish a whole turn around the horizontal pole and that the ropes shall be experiencing a tension sufficient enough for them to be rigid throughout the turn. At the same time we wish to minimalize the initial velocity. Determine the difference of the angular velocity

ω_{1}of

the swing with the child after its return to the bottom dead point and the initial angular velocity

ω_{0}

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