A physics book can be rotated around three mutually perpendicular axes passing s

Question

A physics book can be rotated around three mutually perpendicular axes passing symmetrically through its center. About which of these axes is the rotational inertia smallest? About which is it largest?

a.) Parallel to the width of the book, parallel to the longest dimension

b.) Parallel to the longest dimension, parallel to the width of the book

c.) Parallel to the longest dimension, perpendicular to the covers of the book

d.) Perpendicular to the covers of the book, parallel to the width of the book

e.) Parallel to the width of the book, perpendicular to the covers of the book

f.) Perpendicular to the covers of the book, parallel to the longest dimension.

Explanation / Answer

c.) Parallel to the longest dimension, perpendicular to the covers of the book

About, Longest dimensions, I_W = m*w^2/3

About width, I_L = m*L^2/3

About perpendicular to the covers of the book, I = I_W + I_L

= m*w^2/3 + m*L^2/3

so, I > I_W > I_L

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