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A Yo-Yo with a Brain Yomega (“The yo-yo with a brain”) is constructed with a clever clutch mechanism in its axle that allows it to rotate freely and “sleep” when its angular speed is greater than a certain critical value. When the yo-yo’s angular speed falls below this value, the clutch engages, causing the yo-yo to climb the string to the user’s hand. If the moment of inertia of the yo-yo is 7.4×10−5 kg · m2, its mass is 0.11 kg. and the string is 1.0 m long, what is the smallest angular speed that will allow the yo-yo to return to the user’s hand?
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