Finding the moment of inertia for a hollow cylinder

In summary, to find the moment of inertia for a hollow cylinder with a closed bottom, you can add the moments of inertia of the cylinder and the bottom disk. If the thickness is uniform, you can find the masses of each part by comparing their relative areas. The surface area of the cylinder is Lx2πr and the area of the bottom is πr2.
  • #1
Antares
2
0
I need help finding the moment of inertia for a hollow cylinder with a closed bottom (like a glass of water). My strategy is to add the moments of inertia of the cylinder and the disk but I only have the total mass of the whole object. Is there a way to find the mass of each part or is there another approach to this problem?
 
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  • #2
Just sum the mass as an integral as follows.

[tex]I=\int r^2 dm [/tex]
 
  • #3
Antares said:
Is there a way to find the mass of each part or is there another approach to this problem?
If the thickness is uniform then you can find the masses of the cylinder and bottom by comparing their relative areas. The surface area of the cylinder is Lx2πr; the area of the bottom is πr2.
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by considering the mass distribution of the object around its axis of rotation.

2. How do you calculate moment of inertia for a hollow cylinder?

The formula for calculating moment of inertia for a hollow cylinder is I = ½MR², where M is the mass of the cylinder and R is the radius of the cylinder. It is important to note that this formula assumes the cylinder has a uniform mass distribution.

3. Can the moment of inertia for a hollow cylinder vary?

Yes, the moment of inertia for a hollow cylinder can vary depending on the distribution of mass within the cylinder. If the mass is not distributed uniformly, the moment of inertia will be different.

4. Why is moment of inertia important?

Moment of inertia is important because it helps us understand how an object will behave when it is rotating. It is used in many engineering and physics calculations, such as determining the torque needed to rotate an object or the angular acceleration of a spinning object.

5. How does the moment of inertia differ from the center of mass?

The moment of inertia is a measure of an object's resistance to rotational motion, while the center of mass is the point at which an object's weight is evenly distributed. The two are related, but the moment of inertia takes into account the mass distribution of the object, while the center of mass only considers the object's weight.

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