Moment of inertia of a uniform solid sphere

In summary, the formula for calculating the moment of inertia of a uniform solid sphere is I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius. The moment of inertia of a solid sphere is greater than that of a hollow sphere with the same mass and radius, as the mass is distributed further away from the axis of rotation in a solid sphere. Shifting the axis of rotation will change the moment of inertia, which is directly proportional to the square of the distance between the axis of rotation and the center of mass of the sphere. As the mass or radius of a solid sphere is increased, the moment of inertia also increases due to the further distribution of mass from the
  • #1
david456103
13
0
For calculating I of a uniform solid sphere, why can't we use thin spherical shells? When I try to use spherical shells I get (3/5)MR^2. Every single derivation uses thin cylindrical shells and end up with the correct expression((2/5)MR^2) but they never explain why it is correct to use cylindrical shells and not spherical shells.
Thanks!
 
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  • #2
You certainly can get there via spherical shells, but it produces the same answer: 2/5.
What do you get for the MI of the shell?
 

FAQ: Moment of inertia of a uniform solid sphere

1. What is the formula for calculating the moment of inertia of a uniform solid sphere?

The formula for calculating the moment of inertia of a uniform solid sphere is I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius.

2. How does the moment of inertia of a solid sphere differ from that of a hollow sphere?

The moment of inertia of a solid sphere is greater than that of a hollow sphere with the same mass and radius. This is because the mass is distributed further away from the axis of rotation in a solid sphere, resulting in a larger moment of inertia.

3. Does the moment of inertia of a solid sphere change if the axis of rotation is shifted?

Yes, the moment of inertia of a solid sphere changes if the axis of rotation is shifted. It is directly proportional to the square of the distance between the axis of rotation and the center of mass of the sphere.

4. How does the moment of inertia of a solid sphere change as the mass or radius is increased?

The moment of inertia of a solid sphere increases as the mass or radius is increased. This is because the mass is distributed further away from the axis of rotation, resulting in a larger moment of inertia.

5. Is the moment of inertia of a solid sphere affected by its shape?

Yes, the moment of inertia of a solid sphere is affected by its shape. The moment of inertia depends on the mass distribution of the object, so a sphere with a non-uniform mass distribution will have a different moment of inertia compared to a uniform solid sphere.

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