Two disks arelocated on an axle as shown. The lower disk is initially spinningat

Question

Two disks arelocated on an axle as shown. The lower disk is initially spinningat 50 rad per second, and the upper one is not spinning. The upperdisk then falls onto the lower disk, and they stick together. A) isthere a torque on the lower disk? B)Identify a system for which theexternal torque is zero so that the angular momentum of yoursystem? C) What is the initial angular momentum of your system? D)What is the final angular momentum of your system? Express youranswer in terms of w_f, the final angular velocity of the twodisks.

top disk: m1=7.0 kg
R_2= 1.0m

bottom disk: m2= 20kg
R_2=2.0m

Explanation / Answer

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Every system which is in equilibrium, the net torque is zeroso the angular momentum of the system is conserved.
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Initial momentum is
   L1 = I1 1
   =(1/2)mR21   
   =(1/2)7kg(1m)2 (50 rad/s)
   =175kg m2/s
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  Final angular momentum
   L2 = (1/2) (m1R12+m2R22 ) f
  As momentum is conserved L1 =L2
   175kgm2 /s = (1/2) (m1R12 +m2R22 ) f   
      f = 175kgm2 /s / (1/2) (m1R12 +m2R22 )
   = 4 rad/s

     
   =(1/2)mR21   
   =(1/2)7kg(1m)2 (50 rad/s)
   =175kg m2/s
----------------------------------------------------------------------------------------------------------------
  Final angular momentum
   L2 = (1/2) (m1R12+m2R22 ) f
  As momentum is conserved L1 =L2
   175kgm2 /s = (1/2) (m1R12 +m2R22 ) f   
      f = 175kgm2 /s / (1/2) (m1R12 +m2R22 )
   = 4 rad/s

     
   175kgm2 /s = (1/2) (m1R12 +m2R22 ) f   
      f = 175kgm2 /s / (1/2) (m1R12 +m2R22 )
   = 4 rad/s

     
     

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