The products of inertia are zero when the body is symmetrical about the axes of rotation, such as for a rectangular box or cylinder rotating on their symmetry axis.

Why is product of inertia zero?

A quantity similar to a moment of inertia, but relating to a rigid body and a pair of given perpendicular axes. ... When the coordinate planes are planes of symmetry of the rigid body, the products of inertia are zero.

Can an object have zero momentum and still have inertia?

Momentum is a measure of the kinetic energy of the object. A massive object can have any momentum (at least as long as its velocity is less than light speed) including zero or negative momentum depending on the reference frame and coordinate conventions, but always has positive nonzero inertia.