Question

This book has three symmetry axes through its center, all mutually perpendicular. The book’s moment of inertia would be smallest about which of the three? Explain.

Short answer

The moment of inertia would be the smallest about the y-axis.

Step-by-step solution

Understanding the moment of inertia of a book about the three axes

The moment of inertia of the book is dependent on the distribution of mass about any of the three axes. Greater the mass distribution close to the axis, the greater will be the moment of inertia and vice versa.

Consider that a book is placed horizontally on the table. Determine the axis having the greater moment of inertia of the book.

Representation of the axes of the book

The diagram of the book can be shown as:

Here, the book is placed along the z-axis. So, the concentration of mass close to the z-axis is higher.

Determination of the axis having a higher distribution of mass  

The book is rectangular. The length of the book along the z-axis covers a large distance. The breadth of the book is along the x-axis. The height of the book along the y-axis covers a lesser distance. The distribution of mass of the book is very less close to the y-axis. So, the moment of inertia is less along the same axis.

Thus, the moment of inertia would be the smallest about the y-axis.