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Moment of inertia of a hollow sphere
Intermediate
Thin spherical shell about a diameter.
I = (2/3)mR²A thin spherical shell about a diameter: I = (2/3)mR².
m = 3 kg, R = 0.2: 0.08.
Don't confuse shell with solid.
In more detail
For a thin hollow spherical shell of mass M and radius R about a diameter, I = 2MR²/3. All the mass is at the surface, so it is larger than for a solid sphere.
Real-world uses
- Hollow spheres such as beach balls are harder to spin than solid ones of the same mass.
- Scientists use shell models for planetary rotation.
- A table tennis ball or a hollow football is a thin shell, so its moment of inertia is larger than a solid ball of the same mass.
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Frequently asked questions
Why is the hollow sphere larger than the solid one?
Because its mass is farther from the axis on average, so the moment is larger.
Does thickness matter?
For a thin shell, no. For a thick shell, the moment changes.
Which sphere rolls down a slope faster, solid or hollow?
The solid sphere, because less of its kinetic energy goes into rotation for the same mass and radius.
Related topics in Rotational Motion
Moment of inertia of a ring · Moment of inertia of a disc · Moment of inertia of a solid sphere · Parallel axis theorem · Perpendicular axis theorem · Radius of gyration