The figure below shows three rotating uniform disks that are

The figure below shows three rotating, uniform disks that are coupled by belts. One belt runs around the rims of disks A and C. Another belt runs around a central hub on disk A and the rim of disk B. The belts move smoothly without slippage on the rims and hub. Disk A has radius R; its hub has radius 0.5250R; disk B has radius 0.2250R; and disk C has radius 2.500R. Disks B and C have the same density (mass per unit volume) and thickness. What is the ratio of the magnitude of the angular momentum of disk C to that of disk B? L_c/L_b = .

Solution

Let the angular velocity of A be 2w. Then the angular velocity of C is w (its radius=2xradius of A), of hub is 2w (same as A) and of B is (0.5250R/0.2250R)x2w=14w/3. AM(C)=Iw=0.5(2R)²t(2R)²w and AM(B) =
I(14w/3)= 0.5(0.2250R)²t(0.2250R)²(14w/3). So AM(C)/AM(B)= LC/LB= (2/0.2250) x3/14=13337.78.