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« previous| 4 of 13 | next» Problem 10.84 Part A 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 7.8x10-5 kg m2 its mass is 0.14 kg, and the string is 1.1 m long, what is the smallest angular speed that will allow the yo-yo to return to the user's hand? Express your answer using two significant figures. rad/s Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

The vertical speed is related to the angular speed by v=wr. By conservation of the energy, (starting from rest) we have

0=E=(mv^2) /2 + (Iw^2)/2- mgl

we know that v=0 when it reaches to the users hand. So by substituting the values, we get

(7.8*10^-5 w^2 )/ 2=0.14*9.8*1.1

By solving this equation , we get

w=196.71 Sec^-1

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