What is the Moment of Inertia of a Book Pivoting at One Corner?

[armolinasf]

Homework Statement

Suppose I have a book with dimensions 24 by 27 cm and its being pivoted at one of its corners so that it can swing along a plane parallel to itself. I'm supposed to find the period. But in order to do that I need to know its moment of inertia, would I have to write an integral using the definition of moment of inertia or is there some formula that I'm missing? Thanks

 

[PeterO]

Homework Statement

Suppose I have a book with dimensions 24 by 27 cm and its being pivoted at one of its corners so that it can swing along a plane parallel to itself. I'm supposed to find the period. But in order to do that I need to know its moment of inertia, would I have to write an integral using the definition of moment of inertia or is there some formula that I'm missing? Thanks

If you consider the book to be a point mass, at the centre of mass of the book, the problem will reduce to a simple pendulum.

 

[cepheid]

The...period? Do you mean that the book is hanging vertically and acting as a physical pendulum? Because if it's horizontal, it's not even clear to me that you'd have a periodic motion.

You could integrate to find the moment of inertia, but moment of inertia tables will certainly have equations for the moment of inertia of a thing rectangular slab, and you could use the parallel axis theorem to get this for rotation around one of its corners ("thin" here meaning that you can ignore the third dimension -- the thickness).

See for example, here: http://en.wikipedia.org/wiki/List_of_moments_of_inertia