High School

We appreciate your visit to If tex I AB tex and tex I CD tex are the moments of inertia of a uniform hemispherical shell about axes AB and CD. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

If [tex]I_{AB}[/tex] and [tex]I_{CD}[/tex] are the moments of inertia of a uniform hemispherical shell about axes AB and CD respectively, what is the relationship between these two moments of inertia?

Answer :

Final answer:

The moment of inertia of a uniform hemispherical shell about an axis through a diameter of its base and about an axis through its center (parallel to the base diameter) are identical, both represented by the equation ma².

Explanation:

The moment of inertia of a uniform hemispherical shell about an axis AB (a diameter of its base) can be understood by considering it a part of a full sphere. For a complete sphere, the moment of inertia about any diameter is simply ma², which is the same case for our hemisphere since the distribution of mass is symmetrical about any diameter of the base.

According to the parallel axis theorem if we consider the moment of inertia of the hemisphere about an axis CD (which is parallel to the axis AB and passes through the center of mass), we can express it as Ih = ICM + Mh². Since the axis CD lies through the center, h would be zero, and hence Ih would simply be ICM, which also equals to ma² in case of the hemisphere.

Therefore, whether we consider axis AB or CD for our uniform hemispherical shell, the moments of inertia are the same, defined by the equation ma².

Thanks for taking the time to read If tex I AB tex and tex I CD tex are the moments of inertia of a uniform hemispherical shell about axes AB and CD. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada