Moment of Inertia of multiple bodies in contact

In summary, the overall moment of inertia of cylinders in contact, such as a set of rollers, can be calculated using the usual formula. However, if the focus is on how the setup reacts to torque on a single wheel, the simple sum of the individual moments is likely of interest. This would only be applicable if the axes are fixed and torque is applied to a single wheel.
  • #1
Jeremymu1195
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What is the overall moment of inertia of many cylinders in contact, where each is rotated about an axis through its center of mass. For example, a set of rollers. (See picture)
 

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  • #2
You can apply the usual formula, but if you want to know how they react to torque on a single wheel (instead of torque on the whole setup), you are probably interested in the simple sum of the individual moments.
 
  • #3
Yes, I am interested in how the whole setup reacts to a torque. So the moment of inertia of the whole assembly would be the sum of the moments of the individual parts?
 
  • #4
If those axes are fixed and you apply torque to a single wheel (evaluated around its axis), yes.
 
  • #5
Cool, thank you!
 

Related to Moment of Inertia of multiple bodies in contact

1. What is the moment of inertia of multiple bodies in contact?

The moment of inertia of multiple bodies in contact is a measure of their resistance to rotational motion. It is a property that depends on the mass distribution and geometry of the bodies.

2. How is the moment of inertia of multiple bodies in contact calculated?

The moment of inertia of multiple bodies in contact can be calculated by summing the individual moments of inertia of each body. This can be done using either the parallel or perpendicular axis theorem, depending on the orientation of the bodies.

3. What factors affect the moment of inertia of multiple bodies in contact?

The moment of inertia of multiple bodies in contact is affected by the mass distribution, shape, and orientation of the bodies. Generally, the farther the mass is from the axis of rotation and the greater the mass, the higher the moment of inertia will be.

4. How does the moment of inertia of multiple bodies in contact relate to rotational motion?

The moment of inertia of multiple bodies in contact is directly related to the angular acceleration of the bodies. A higher moment of inertia will result in a slower rotational motion for a given torque, while a lower moment of inertia will result in a faster rotational motion.

5. How can the moment of inertia of multiple bodies in contact be used in real-world applications?

The moment of inertia of multiple bodies in contact is a crucial factor in designing and analyzing rotating systems, such as engines, turbines, and flywheels. It is also important in understanding the stability and control of objects in motion, such as satellites and vehicles.

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