Three Disks Coupled by Two Belts

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SUMMARY

The discussion focuses on calculating the ratio of angular momentum between two disks, B and C, coupled by belts to a central disk A. Disk A has a radius of R, disk B has a radius of 0.2000R, and disk C has a radius of 1.500R. The relevant equations include angular momentum (L = mvr) and the moment of inertia for a disk (I = (mr^2)/2). The key insight is that the density of disks B and C, which are uniform and of the same thickness, will influence their mass and thus their angular momentum calculations.

PREREQUISITES
  • Understanding of angular momentum (L = mvr)
  • Knowledge of moment of inertia for disks (I = (mr^2)/2)
  • Familiarity with the concept of uniform density in physics
  • Basic grasp of rotational motion and angular speed
NEXT STEPS
  • Calculate the angular momentum for disk B using its radius and density
  • Calculate the angular momentum for disk C using its radius and density
  • Explore the relationship between angular speeds of coupled disks
  • Investigate the effects of varying densities on angular momentum ratios
USEFUL FOR

Students studying rotational dynamics, physics educators, and anyone interested in understanding angular momentum in coupled systems.

efitzgerald21
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Homework Statement


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 0.6000R; disk B has radius 0.2000R; and disk C has radius 1.500R. 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)=?
Image: http://www.webassign.net/hrw/W0249-N.jpg

Homework Equations


L=mvr=Iw (w is angular speed)
I(disk)=(mr^2)/2


The Attempt at a Solution


Honestly I have no clue how to even start this...
I think that the density will somehow give me mass to plug into equation for I, which can then be plugged into L. But I don't know how to get w or v and without those I don't know how to get L.
 
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Could the w's for each disk all be directly proportional to one another?

I think you are right about the density.
 

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