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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



7 years ago

Answers : (3)

AKASH GOYAL AskiitiansExpert-IITD
419 Points

Dear Pranay

Plz see the pic for solution.

All the best.




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7 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)








7 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

7 years ago
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