Two disks are located on an axle as shown in the figure below. The lower disk is

Question

Two disks are located on an axle as shown in the figure below. The lower disk is initially spinning at 33 rad/s, and the upper one is not spinning. The upper disk then falls onto the lower disk, and they stick together.

(a) Is there a torque on the lower disk?  

On the upper disk?  

(c) What is the initial angular momentum of your system?
kg · m2/s

(d) What is the final angular momentum of your system? Express your answer in terms of f, the final angular velocity of the two disks. (Recall that f has units of rad/s and angular momentum will have units of kg · m2.

f

(e) Find f.

rad/s

Explanation / Answer

(a) Torque = I

      Lower disc experiences torque as it rotates.

(b)   Since upper disc is at rest initially, there is no torque experienced by the it. However, it experiences torque    after it falls onto the lower disc and spin with it.

(c) initial angular momentum of the system is onlly due to the rotating disc i.e. the lower disc

      1 = 33 rad/se

     Initial Angular momentum = I1 1 = {(0.5) m1 r12 } l   = (0.5) * 20 * 22 * 33 = 1320 kgm2s-1

(d) I1 = {(0.5) m1 r12 } = (0.5) * 20 * 22 = 40 kgm2

     I2 = { (0.5) m2 r22 } = (0.5) * 7 * 12 = 3.5 kgm2

since both of the discs spin with a common angular velocity f   

Final angular momentum of the system = (I1 + I2) f    = (40 + 3.5)f = 43.5 f

(e) From conservation of angular momentum

    Intial angular momentum = Final angular momentum

   1320 = 43.5 f

f = 30.34 rad/s

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