The figure shows three rotating, uniform disks that are coupled by belts. One be

Question

The figure 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 0.438R; disk B has radius 0.285R; and disk C has radius 2.20R. Disks B andC 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?

Explanation / Answer

velocit of belt will be same. ( v = w*r = constant )

for A and B :

0.438R * wA = 0.285R * wB

wA = 0.651 wB

for A and C:

R*wA = 2.20R*wC

wA = 2.20wC

so 0.651 wB = 2.20wC

wB = 3.38 wC   ..... (i)

angular momentum = Iw

Ib = (pi x (0.285R)^2) (0.285R)^2 /2    ....(ii)

Ic = (pi x (2.20R)^2) (2.20R)^2 /2 ..... (iii)

Lc / Lb = (IcwC) / (Ib wB)

   = ( (pi x (2.20R)^2) (2.20R)^2 /2 )(wC) / ((pi x (0.285R)^2) (0.285R)^2 /2)(3.38wC)

= 1050.50

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