Thick cylindrical ring find inertia help

In summary, the thick cylindrical ring has an outer radius of 0.318 meters, an inner radius of 0.29 meters, and a mass of 10 kg. The moment of inertia of this cylinder about its central axis can be calculated using the formula I = 1/2 (MR^2 - mr^2), where M is the total mass of the ring and m is the mass of the removed thinner cylinder.
  • #1
blackbyron
48
0

Homework Statement



A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis?

Homework Equations



I = (.5)(m)(ri^2+ro^2)

The Attempt at a Solution


I tried to use hollow cylinder formula, but the answer says it's wrong.
I don't know if I use the right inertia formula. I don't know if thickness is the outer radius. I confused.

Thanks
 
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  • #2
The thickness is the difference between the outer radius and the inner one. Use the formula of the solid cylinder. The thick cylindrical ring is made from a solid cylinder by removing a thinner cylinder from its inside.

ehild
 
  • #3
Ah okay, yeah cause I thought the formula I mention is the one I have to use. But thanks for your help.
 
  • #4
Sorry, but I think I'm lost here. How does solid cylinder relate to the thick cylindrical ring? Because when I use solid cylinder formula, it didn't work on the answer tho.

And also

"The thick cylindrical ring is made from a solid cylinder by removing a thinner cylinder from its inside."
So you're saying that the inner solid cylinder is removed right? And the thick cylindrical ring is the only thing left. Is that correct.


outer radius .29meters, thickness is .028m mass is 10 kg.

I = (1/2)(M)(R)^2
 
  • #5
blackbyron said:
So you're saying that the inner solid cylinder is removed right? And the thick cylindrical ring is the only thing left. Is that correct.


outer radius .29meters, thickness is .028m mass is 10 kg.

I = (1/2)(M)(R)^2

The outer radius is R=(0.29 + 0.028) m, the inner radius is r=0.29 m. The mass of the ring is 10 kg. If the mass of the thinner cylinder is m, that of the thick one is

M=10+m.

The density of both cylinders is the same as that of the ring.

The moment of inertia is

I = 1/2 (MR2-mr2)

ehild
 
  • #6
Oh I see, I forgot to add the thickness by radius to get the outer radius.

Sorry about that

Thanks for your help

Now I'm getting it.
 

Related to Thick cylindrical ring find inertia help

1. What is a thick cylindrical ring?

A thick cylindrical ring is a solid, circular object with a height that is significantly larger than its radius. It can be made of various materials, such as metal or plastic, and is often used in engineering and construction projects.

2. What is the concept of inertia?

Inertia is a property of matter that describes its resistance to changes in motion. In other words, an object with more inertia will require more force to change its state of motion compared to an object with less inertia.

3. How is inertia related to a thick cylindrical ring?

Inertia is related to a thick cylindrical ring because the shape and mass distribution of the ring determine its moment of inertia, which is a measure of its resistance to rotational motion. The thicker and denser the ring, the greater its moment of inertia and thus its resistance to changes in rotational motion.

4. Why is it important to find the inertia of a thick cylindrical ring?

Finding the inertia of a thick cylindrical ring is important in various engineering and physics applications. It helps in determining the stability and strength of structures, predicting the motion of rotating objects, and designing efficient machinery.

5. How can one calculate the inertia of a thick cylindrical ring?

The inertia of a thick cylindrical ring can be calculated using the formula I = 1/2 * m * (r1^2 + r2^2), where m is the mass of the ring and r1 and r2 are the inner and outer radii, respectively. Alternatively, it can also be found using specialized computer software or through physical experimentation.

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