Question

2. A circular shaft is mounted in a bearing as shown. There is a small gap between the stationary inner shaft and the outer rotating bearing filled with a viscous, incompressible Newtonian fluid. The shaft turns with a constant rotation rate o (in rad/sec) due to the downward motion of the attached weight pulling on the cord attached to a the outer bearing (see figure) of radius R Hint: If the gap between the shaft and bearing is small compared to the shaft radius, a linear velocity profile results. a The rotation rate o depends on the outer bearing radius R and several other independent variables listed in the table. There are three missing independent variables in the 1 column Fill these in Carefully define each variable in words and with a mathematical symbol If the Your Analysis Does Your Independent Prediction Prediction: Prediction Match the Analysis Prediction? Independent Variable Variables From Physical Intuition (with all other parametersDoes theDoes your Write YES to held constant angular answer confirm that velocity ω|ω (from part1 this is true. increase) or b) decrease (I) increase (1) or or stay the decrease (I) same Θ? | orstay the same ()? Outer bearing adius R nner bearing radins R Mass Hanging b) Find an expression (equation) for the rotation rate variables in part a). as a function of your listed independent c) Fill in the rest of the above table. t d the fuid gap thickness R will the rotation rate ω -Ri is decreased (with all other relevant parameters held constant), Increase Decrease Stay the same e Why? e.g. clearly describe your physical reasoning for part (d). Note: Do not simply use your equation from part (b) to answer this. Discuss the physics' which leads to your answer. If the gravitational acceleration is decreased, by moving the bearing to the Moon, for example (with all other relevant parameters held constant), will the rotation rate ω Increase Decrease Stay the same g) Why? eg, clearly describe your physical reasoning for part(). Note: Do nof simply use your equarion from part (b) to answer this. Discuss the physics which leads to your answer. The bearing extends into the paper Angular veloci Ri Ri Stationary Fluid Weight

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