Question

d) If the fluid gap thickness R -R is dacreased (with all other relevant parameters held constant), will the rotation rate 2 A circular shaft is mounted in a bearing as shown. There is a smal pap between the stationary inner shaft and the outer rotating bearing filled with a viscous, incompreasible Newtonian fluid. The sha turns with a constant rotation rate o in radsec) due to the downward motion of the attached weight pulling oa the ccrd attached to a the outer hearing (see figure) of radius R Stay the same ncrease Decrease e) Why? e.g clearly describe yuur pyceaning for partd Noe: Do o simply e yow eurmcation fram part fby to answer this. Discars the pirysics which laaay towor answe Hint: If the gap between the shaft and bearing is small compared tn the shaft radius, a linenr velocity prufile results. q) The rotation rate ω depends on the outer bearing radius R. and several other independent variables listed in the table. There are twee missing ndependent variabes in the cofama F these in Carefinly define each variale n words and with a marhematical symbl If the Does Your If he gravitational acceleration is decreased, by moving the bearing to the Moon, for example (with all other relevant paramecers held constant), will the ratation rate Independe Variable Variables Match the Increase Decrease Stay the same Intuition: otherDoes parameters Dos Prediction? Doesyour Write YES to answer confirm that g) Why? eg clearly deacrbe your prysical reasoning for part (. Nofe: Do nof simply ue yow equaion pro part b to awer this. Discuse (he phyrics which leais to yoar answer (from part this is true velocity increase (t) orb) decrease (↓) | ncrease (t) or or stay the decrease () or stay the same (? Onter bearing ner bearing The bearing extecds intu the puper Angalar velocity R2 Stationary Fluid b) Find an expression (equation) for the rotation rate ω as a function of your listed indepee dest variables in part a). c) Fill in the rest of the above table

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.