# Three Disks Coupled by Two Belts

• efitzgerald21
In summary: We can use it to find the mass of each disk, which we can then plug into the equation for moment of inertia (I). Since the disks are rotating without slippage, we can assume that the angular speeds (w) are equal for all three disks. Therefore, we can set up a ratio using the equation for angular momentum (L=mvr). In summary, we can use the density to find the mass of each disk, which we can plug into the equation for moment of inertia. Since the disks are rotating without slippage, we can assume that the angular speeds are equal for all three disks and set up a ratio using the equation for angular momentum.
efitzgerald21

## 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.

Could the w's for each disk all be directly proportional to one another?

I think you are right about the density.

## 1. What is the purpose of coupling three disks with two belts?

The purpose of coupling three disks with two belts is to transfer power and motion between the disks. This allows for synchronized rotation and can also increase torque and speed.

## 2. How are the belts connected to the disks?

The belts are typically connected to the disks using a pulley system. This involves wrapping the belts around the disks and securing them with tension to ensure proper rotation and power transfer.

## 3. What materials are commonly used for the belts?

The belts used for coupling three disks are typically made of rubber or synthetic materials such as polyurethane. These materials are flexible and durable, making them ideal for power transmission.

## 4. How do the belts affect the overall performance of the system?

The belts play a crucial role in the performance of the system. They determine the amount of power and torque that can be transferred between the disks, as well as the speed of rotation. Therefore, choosing the right type and size of belt is essential for optimal performance.

## 5. What are some common applications of three disks coupled by two belts?

This type of coupling system is commonly used in machinery and equipment that requires synchronized rotation of multiple components. Some examples include conveyor systems, printing machines, and automotive engines.

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