Moment of Inertia: Hoop

The moment of inertia of a hoop or thin hollow cylinder of negligible thickness about its central axis is a straightforward extension of the moment of inertia of a point mass since all of the mass is at the same distance R from the central axis.

For mass M = kg
and radius R = cm
the moment of inertia is
I = kg m^2
For a thin hoop about a diameter in the plane of the hoop, the application of the perpendicular axis theorem gives
I(thin hoop about diameter) = kg m^2

Show effect of hoop thickness

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Thick Hoops and Hollow Cylinders




 For mass M = kg,
internal radius a = cm
and external radius b = cm,
the moment of inertia I = kg m^2.
This may be compared with a solid cylinder of equal mass where I(solid) = kg m^2, or with a thin hoop or thin-walled cylinder where I(thin) = kg m^2.
The moment of inertia of a hollow circular cylinder of any length is given by the expression shown.

Show hollow cylinder development

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Moment of inertia concepts
 
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