Hollow Sphere Moment of Inertia Help

In summary, the problem involves finding the moment of inertia of a hollow sphere of given mass and radii. The attempt at a solution used the formula for a solid sphere, but the correct approach is to compute the moment of inertia for both the inner and outer spheres and subtract them to account for the hollow space. The density of the material must also be taken into consideration.
  • #1
George3
31
0

Homework Statement


A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center?


Homework Equations





The Attempt at a Solution


I = 2/3 MR^2 for a hollow sphere so i did this:
2/3 (15) (.18^2) = .32 kg m^2

But this is wrong the answer is .24 kg m^2.
Any thoughts?
 
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  • #2
George3 said:

Homework Statement


A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center?


Homework Equations





The Attempt at a Solution


I = 2/3 MR^2 for a hollow sphere so i did this:
2/3 (15) (.18^2) = .32 kg m^2

But this is wrong the answer is .24 kg m^2.
Any thoughts?

Have you tried computing the moment of inertia of a solid sphere of radius 18 cm and subtracting from it the moment of inertia of a solid sphere with a radius of 12 cm? In other words "scooping" out the center of the original sphere to create your object?
 
  • #3
BUMP... FINAL TOMORROW NEED HELP ON THIS
I really need help on this. And to the previous poster the moment of inertia of a hollow sphere is bigger than that of a solid so your method would not work...right?
 
  • #4
George3 said:
BUMP... FINAL TOMORROW NEED HELP ON THIS
I really need help on this. And to the previous poster the moment of inertia of a hollow sphere is bigger than that of a solid so your method would not work...right?

Well, I just computed your moment of inertia by doing what I told you to do and got the right answer. Your mistake is confusing a sphere with a spherical portion of the interior removed with a spherical shell.

By the way, you will have to compute the density of the material out of which the object is made.
 
  • #5
AEM said:
Well, I just computed your moment of inertia by doing what I told you to do and got the right answer. Your mistake is confusing a sphere with a spherical portion of the interior removed with a spherical shell.

By the way, you will have to compute the density of the material out of which the object is made.

So did you take (2/5)MR^2 for both radii and then subtract the two moments of inertia? Which formula for I did you use??
 
Last edited:
  • #6
George3 said:
So did you take (2/5)MR^2 for both radii and then subtract the two moments of inertia? Which formula for I did you use??

What you do is use [itex] I = \frac{2}{5}Mr^2 [/itex] for each sphere. This is why you need the density of the material. You have to know the mass of the smaller sphere and the mass of the larger sphere. You also have to use the appropriate radius for each. And, yes you subtract the moments of inertia that you compute.
 
  • #7
I was able to get it thanks for the insight it helped a lot.
 

Related to Hollow Sphere Moment of Inertia Help

What is a hollow sphere's moment of inertia?

The moment of inertia of a hollow sphere is a measure of its resistance to rotational motion. It is a mathematical property that describes how mass is distributed around the axis of rotation.

How is the moment of inertia of a hollow sphere calculated?

The moment of inertia of a hollow sphere can be calculated by using the formula I = (2/3)MR^2, where I is the moment of inertia, M is the mass of the sphere, and R is the radius of the sphere.

What factors affect the moment of inertia of a hollow sphere?

The moment of inertia of a hollow sphere is affected by its mass and radius. The larger the mass and radius, the larger the moment of inertia will be.

Why is the moment of inertia important?

The moment of inertia is important because it helps to determine how an object will behave when subjected to rotational motion. It is also used in calculations for angular momentum and torque.

How does the moment of inertia of a hollow sphere compare to other shapes?

The moment of inertia of a hollow sphere is different from other shapes, such as a solid sphere or a cylinder. This is because the mass is distributed differently in these shapes, resulting in different moment of inertia values.

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