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 ω (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 R2, 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 Does Your Independent Predictio Prediction: Prediction Match the Analysis Prediction? IndependenVariable Variables Physical Intuition: (with all other parameters Does held constant angular the Does your answer forconfirm that Write YES to velocity ω|ω(from part! this is true. increase (1) or b) decrease () increase (1) or or stay the decrease (I) same (? or stay the ame? Outer bearing radius R Inner bearing radtus R Mass Hanging b) Find an expression (equation) for the rotation rate o as a function of your listed independent variables in part a). c) Fill in the rest of the above table. d) If the fluid gap thickness R - R is decreased (with all other relevant parameters held constant), will the rotation rate Increase Stay the same Decrease e) Why? eg. clearly describe your physical reasoning for part (d). Note: Do not simply use your equation from part (b) to nwer this. Discuss the physics' which leads to your answer. D 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 Stay the same Increase Decrease g Why? eg elearly describe your physical reasoning for part (). Note: Do not simply wse your equation from part (b) to answer this. Discuss the physics' which leads to your answer. The bearing extends into the paper Angular velocity Ri R2 Stationary Fluid Weight

Answer 1

So lution: Civen that- stationary Duter nadius of beaig Jnnes A Angular velouity Fluid Area af comtact A weight of 1ock, W Jemg when, weight oes down due to belan ced by ravity fore of positeto tha ythis &hear will be gravity shear forre) FS ie. TA A R-RI Angular veloity Re-RI fluid thicleness CRe-R) decreases If (d) Rotation prate decreases. when thickness af fluid Layes Phy 8ically decreases angulas velecity wA (Re7RI) 9 becomes

If gravitation al acceleration is decreased, The 10tation ate in cseases Physical neasonr is that G) The notation is clockwise wh the weight of the block fshear force dominates and thus notation decreases and nate ihcrea ses.