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D) You are playing Wheel of Fortune and pull down on the big uniform cylinder of...

D) You are playing Wheel of Fortune and pull down on the big uniform cylinder of mass M and radius R (take clockwise to be positive, as shown). You apply a constant force F to the edge of the wheel to spin for fortunes. Throughout your pulling on the wheel, you manage to keep the force perpendicular as it rotates. Assume that there is no friction anywhere and that the wheel is at rest before you start pulling. (i) Find the torque that you apply to the wheel and use it to determine the angular acceleration of the wheel. (ii) How much work do you do to the wheel when pulling on it through ∆θ radians? (iii) Let your answer to (ii) be Wyou. Using the work-energy theorem, find the angular speed of the wheel when you have pulled it through ∆θ radians. Answer in terms of Wyou, M and R.

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