A boy standing firmly spins the girl sitting on a circular "dish" or sled in a circular path of radius r₀ = 3 m such that her angular velocity is θ̇₀ = 0.1 rad/s. If the attached cable OC is drawn inward such that the radial coordinate r changes with a constant speed of ṙ = -0.5 m/s, determine the tension it exerts on the sled at the instant r = 2 m. The sled and girl have a total mass of 50 kg. Neglect the size of the girl and sled and the effects of friction between the sled and ice. First show that the equation of motion in the θ direction yields de a_θ = rθ̈+ 2ṙθ̇ = (1/r) d/dt(²θ̇) = 0. When integrated, r²θ̇ = 20 C, where the constant C is determined from the problem data.

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T 1 m 0 r = 2 m r = 3 m C