
422 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
5. Consider a rigid body that is in the form of a plane lamina of any shape. If the lamina is
in the xy-plane, and I
x
, I
y
, and I
z
denote the moments of inertia about the x-, y-, and z-axes,
respectively, prove that
I
z
= I
x
+ I
y
.
This is known as the perpendicular axis theorem for a plane lamina.
6. (a) Find the inertia tensor for a uniform square plate of side a and mass m about a diagonal
in a coordinate system Oxyz, where O is at one corner and the x- and y-axes are along
two edges.
(b) Find the angular momentum about the origin for the plate just mentioned in (a) when
it is ...