The figure below shows three rotating, uniform disks that are coupled by belts.
ID: 585187 • Letter: T
Question
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 = .Explanation / Answer
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.