How to Calculate the Moment of Inertia of an Assembly?

In summary, the conversation is about calculating the mass moment of inertia of an assembly consisting of a ring with several rectangular boxes mounted around its periphery. The person is seeking help in calculating the inertia of the assembly.
  • #1
vscid
5
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I am trying to find out how to calculate the
mass moment of inertia of an assembly.
I have basically a ring 7 inch ID,11 Inch OD
and 1 inch thick.

On this ring I have several rectangular boxes mounted
of various sizes around its periphery (screwed.)
This ring will rotate about its axis along with those
boxes of different sizes.
How do I calculate the inertia of the assembly?

please help.

Sid
:cry:
 
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  • #3
This is a HW/Schoolwork-type question. So it belongs in the HW/Coursework forum even if it isn't a homework assignment.

Zz.
 

Q1: What is the definition of moment of inertia?

Moment of inertia is a measurement of an object's resistance to changes in its rotational motion. It is the sum of the products of each individual particle's mass and its distance from the axis of rotation squared.

Q2: How is moment of inertia calculated for a point mass?

For a point mass, the moment of inertia is equal to the mass of the object multiplied by the square of the distance from the axis of rotation.

Q3: What is the formula for calculating moment of inertia for a continuous object?

The formula for calculating moment of inertia for a continuous object is ∫r²dm, where r is the distance from the axis of rotation and dm is the mass of an infinitesimally small element of the object.

Q4: How does the distribution of mass affect moment of inertia?

The distribution of mass affects moment of inertia as it determines the distances of the individual particles from the axis of rotation. Objects with more mass concentrated further away from the axis of rotation will have a larger moment of inertia compared to objects with the same mass but concentrated closer to the axis.

Q5: What are some real-world applications of calculating moment of inertia?

Moment of inertia is used in various engineering and physics applications, such as designing rotating machinery, analyzing the stability of structures, and understanding the behavior of objects in rotational motion. It is also important in sports, such as figure skating, where skaters use their body's moment of inertia to perform spins and jumps.

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