:You don't actually need the moment of inertia tensor for this problem, but it is useful as a way of double-checking my understanding of the definitions used above.
22.
Analogous to mass times acceleration, the moment of inertia tensor depends on the distribution of mass about the axis of rotation, and the angular acceleration is the rate of change of angular velocity,
23.
Calculations involving acceleration, angular acceleration, angular velocity, angular momentum, and kinetic energy are often easiest in body coordinates, because then the moment of inertia tensor does not change in time.
24.
To account for rotational energy and momentum, we must describe how force is applied to the object using a moment, and account for the mass distribution of the object using an inertia tensor.
25.
I can do it in the case when the inertia tensor is singular ( so all the mass lies on the vector \ mathbf { e } ) but not in the more general case.
26.
In general, then, there will be three additional degrees of freedom corresponding to the rotational motion of the molecule, ( For linear molecules one of the inertia tensor terms vanishes and there are only two rotational degrees of freedom ).
27.
:: "'Inertia Tensor "': I've been silent recently, because I've been in this cyclical wheel for a long time, as see no point in repeating myself on the talk page.
28.
In general, "'L "'= "'I�� "'is substituted and the time derivatives are taken realizing that the inertia tensor, and so also the principal moments, do not depend on time.
29.
Where \ mathbf { I } is the central inertia tensor, \ vec { \ omega } is the angular velocity vector, and \ tau _ { j } is the moment of the " j " th external force about the mass center.
30.
If one also diagonalizes the rigid body's moment of inertia tensor ( with nine components, six of which are independent ), then one has a set of coordinates ( called the principal axes ) in which the moment of inertia tensor has only three components.
