Two disks are rotating about the same axis. Disk A has a moment of inertia of 6.

Question

Two disks are rotating about the same axis. Disk A has a moment of inertia of 6.43 kgm2 and an angular velocity of +6.07 rad/s. Disk B is rotating with an angular velocity of -7.53 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocity of -3.23 rad/s. The axis of rotation for this unit is the same as that for the separate disks. What is the moment of inertia of disk B?

*please show all the work you do and use appropriate units! Thanks!*

Explanation / Answer

here

Angular momentum of disk A is L1 = j1 * w1,where j1=6.43, w1= 6.04;

Angular momentum of disk B is L2 = j2 * w2,where j2 is moment of inertia in question, w2=-7.53;

then

Angular momentum of linked disks is L3 = (j1 + j2) * w3, where w3=-3.23;

Total momentum conserves! That is L3 = L1 + L2; or;
(j1 + j2) * w3 = j1 * w1 + j2 * w2, hence
j2 = j1 * (w1

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