Mass Moment of inertia of a cylinder with 4 holes?

In summary, the conversation discusses a problem involving a 6-inch long cylinder with a 24-inch diameter and a weight density of 490 lb/ft^3. The solution involves finding the mass and moment of inertia for the cylinder with holes drilled symmetrically around a 10-inch diameter circle. The suggested approach is to convert the weight density into mass density and then use the parallel axis theorem to calculate the moment of inertia for the entire cylinder.
  • #1
qpham26
56
0

Homework Statement



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 Thanks for your time and consideration.
Appreciate it!

Homework Equations


The Attempt at a Solution


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?
 
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  • #2
That is a correct approach.

ehild
 
  • #3
Thanks and for the mass of the cylinder, the unit is slug right?

Thanks again.
 
  • #4
I am sorry, I am not familiar with imperial units. But Wikipedia says it is slug.
The slug is a unit of mass associated with Imperial units. It is a mass that accelerates by 1 ft/s2 when a force of one pound-force (lbF) is exerted on it.

http://en.wikipedia.org/wiki/Slug_(mass )

ehild
 
Last edited by a moderator:
  • #5
qpham26 said:

Homework Statement



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


Thanks for your time and consideration.
Appreciate it!

Homework Equations





The Attempt at a Solution


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?
yah...
this only is the right way of solving it.
 
Last edited by a moderator:

FAQ: Mass Moment of inertia of a cylinder with 4 holes?

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

The formula for calculating the mass moment of inertia of a cylinder with 4 holes is: I = ½mr² + ½m(r² + l²).

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

The location of the holes does not affect the mass moment of inertia of the cylinder, as long as they are evenly distributed around the axis of rotation. This is because the mass moment of inertia is a measure of an object’s resistance to rotational motion, and the location of the holes does not change the overall shape and distribution of mass of the cylinder.

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

No, the mass moment of inertia of a cylinder with 4 holes cannot be negative. It is always a positive value, as it represents the object’s resistance to rotational motion and cannot have a negative magnitude.

4. How does the mass moment of inertia of a cylinder with 4 holes compare to a solid cylinder?

The mass moment of inertia of a cylinder with 4 holes is generally lower than that of a solid cylinder with the same mass and dimensions. This is because the holes reduce the overall mass and therefore, the resistance to rotational motion of the object.

5. Is the mass moment of inertia of a cylinder with 4 holes affected by the size of the holes?

Yes, the mass moment of inertia of a cylinder with 4 holes is affected by the size of the holes. Larger holes will result in a lower mass moment of inertia, as they reduce the overall mass of the object more significantly compared to smaller holes.

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