# Mass Moment of inertia of a cylinder with 4 holes

• qpham26
In summary, the conversation discusses a problem involving a 6 inch cylinder with a diameter of 24 inches and a given weight density of 490 lb/ft^3. The solution involves finding the mass of the cylinder without holes, the mass of each hole, and using the parallel axis theorem to calculate the moment of inertia for both the holes and the solid cylinder. The final step involves converting to mass density and checking for any mistakes.
qpham26
Hi I was reviewing for my final and I came across this problem:

Problem:
Basically there is a 6in long cylinder with dia = 24in
Given weight density: 490 lb/ft^3

Each Hole is drilled symmetrically, each has 6in dia and equally space around a 10in dia circle concentric with the cylinder.

This is the picture of the frontview of the cylinder: https://lh4.googleusercontent.com/-8m1r4npC7cg/T11OqGF6qhI/AAAAAAAAABY/4v2HCrEqhd4/s333/cyinder.png
Approach
So what I would do is:
-First get that weight density into mass density by dividing it by 32.2
-Then find the mass of the cylinder without holes.
-Find mass of each holes.
-calculate the M of I of each hole about the center axis (parallel axis theorem)
-calculate the M of I of the whole solid cylinder (no holes)
-subtract the M of I of the holes from the whole cylinder

Will I get the correct answer based on the technique above?
Is there any mistake?

Thanks for your time and consideration.
Appreciate it!

What you are given is a specific weight, 490 lb/ft^3, and I would suggest that you work with that value until the last step, converting to mass only in the last step. This will preserve a little bit of accuracy (less rounding).

Otherwise, your procedure is fine; go to it!

## 1. What is the formula for calculating the mass moment of inertia of a cylinder with 4 holes?

The mass moment of inertia of a cylinder with 4 holes can be calculated using the formula I = ½mr², where I is the moment of inertia, m is the mass, and r is the radius of the cylinder.

## 2. How does the placement of the holes affect the mass moment of inertia of the cylinder?

The placement of the holes can significantly affect the mass moment of inertia of the cylinder. If the holes are closer to the center of the cylinder, the moment of inertia will decrease. If the holes are farther away from the center, the moment of inertia will increase.

## 3. Can the mass moment of inertia of a cylinder with 4 holes be negative?

No, the mass moment of inertia cannot be negative. It is a measure of an object's resistance to rotational motion and therefore must always be a positive value.

## 4. How does the mass of the cylinder and the holes affect the mass moment of inertia?

The mass of the cylinder and the holes both contribute to the overall moment of inertia. The larger the mass of the cylinder and the holes, the greater the moment of inertia will be.

## 5. Is the mass moment of inertia of a cylinder with 4 holes the same as a solid cylinder with the same mass?

No, the mass moment of inertia of a cylinder with 4 holes will be different from a solid cylinder with the same mass. The presence of the holes changes the distribution of mass and therefore affects the moment of inertia.

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