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pranay -askiitians expert Grade: 12
        

a centrifuge consists of 4 solid cylindrical containers , each of mass m at radial distance r from the axis of rotation. time t is required to bring the centrifuge to an angular velocity W from rest under a constant torque T applied to the shaft. the radius of each container is A and the mass of the shaft and arms is small compared to m. then t=.............................


ans= 2m(a2+2r2)W/T


fig:-  


312_23440_scan0008.jpg

6 years ago

Answers : (3)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

Dear Pranay


Plz see the pic for solution.


All the best.


AKASH GOYAL


AskiitiansExpert-IITD


 


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1143_23499_Photo-0106.jpg

6 years ago
vikas askiitian expert
510 Points
										

net torque on the shaft is given...


now we can find net angular accleration of the system by


         T=I(alfa)                         (T -torque,alfa - angura accleration and I is total moment of inertial of system )


 alfa = T/I .........1


 


moment of inertial of any of cylender about the axis of rotation is I1


 I1 = I(about its own axis) + I(about axis of rotation)


I1 = ma2 /2 + md2                     ( a is radius of cylender and r is perpendicular distance from axis of rotation)


  I


 


 


 


 


 


 



6 years ago
vikas askiitian expert
510 Points
										

I posted the comlete solution but i dont know why remaining part is not appearing ...


here is the remaining solution remaining solution :


                  I1 = I (about axis of rotation) + I(abot its own axis)


                  I1 = mr2 + ma2 /2                          ( Icom =ma2 /2 )


  total moment of inertia is 4I1


         I = 4I1 = 4mr2 + 2ma2     


for constant torque we can use this eq


                     W =W0 + (alfa)t                             (alfa is angular accleration)


                t=W/alfa                         (w0  is 0 )


                t = WI/T


               t = 2m(a2 + 2r2 )W/T

6 years ago
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