In terms of a standard set of coordinates (x,y,z) fixed to planet Earth, find the equation described by the string of a pendulum at equilibrium in Boston, MA.

In this chapter we are going to consider a rigid bodv in rotation. |Dur first topic will be finding the relationship between the vector angular momentum and the vector angular velocitv. Remember that, from elementarv mechanics, there is a linear relationship between the two vectors, given bv: _"s LQ=Icf where the constant of proportionalitvr is the object's moment of inertia about the axis of rotation. However, this is onlv true if we consider the following two situations: ii] Flat objects rotating about a fixed axis of rotation perpendicular to the object. where we take the point of reference Q at the intersection between the axis of rotation and the plane of the object. iii} Svmmetrical objects rotating about fixed axes of svmmetrv. Then the point of reference Q can be taken anwvhere and the result is the same. We are going to see in this lecture that actuallv this relationship m BE MADE GENERAL if we substitue the moment of inertia I {which plavs the role as a scalar quantitv} bv a 3X3 svmmetric matrix, that we will call the TENSDR 0F INERTIA. thsicallv, the tensor of inertia is a tensor of rank 2. which is a quantitv that behaves under coordinate transformations as the the product of two vector quantities