Inertia tensor Definition and 64 Threads

Hi all, this is my first post. I'm under the gun at the moment because we were just told yesterday to expect a similar problem to the one below on our final, yet we were not taught how to work such a problem in class. (Our teacher does not write the final hence the discrepancy.) I have a...

Does a free electron have a moment of inertia tensor? :blushing:

Homework Statement In Cartesian coordinate system are two point masses of mass m connected with massless rod. Masses are in (0,r,0) and (0,-r,0). a) Find the moment of inertia tensor. b) Points were rotated in OXY plane such that angle between rod and Y-axis is \vartheta (new cooridnates of...

Hello, Recently I was using multibody dynamics software at work and when I ran the simulation it warned me that the values that I specified for the inertia tensor of one of the bodies was physically impossible. It turned out that I had mistyped one of the values and it was an easy fix, but...

1. Problem I need to find the principal moments of inertia about the center of mass of a flat rigid 45 degree right triangle with uniform mass density. 2. Useful Formulae I_{xx}=\int_{V} \rho (r^{2}-x^{2}) dV I_{jk}=\int_{V} \rho (r^{2} \delta_{jk} - x_{j} x_{k}) dV 3. Attempt at a...

Homework Statement What is the relationship between the inertia tensor and the rotational inertia? How can a second-rank tensor describe the same thing as a scalar? Is their a formula to go between one and the other i.e. if I have an inertia tensor for a rigid body rotating about some axis...

[SOLVED] Moment of Inertia tensor SETUP, not to difficult but can't figure it out Homework Statement a) For a cylinder of mass M, radius R and height h, calculate the inertia tensor about the center of mass. What are the principal axes? Homework Equations The Attempt at a Solution...

Homework Statement Find the center of mass and inertia tensor at the CoM of the following triangle. Density of the triangle is \sigma(x,y) = x and y=3-3/4x . Homework Equations Find the inertia tensor at the origin (x,y,z) and apply the parallel axis theorem...

what is the difference between moment of inertia and moment inertia tensor?

I have a cylinder, for which i want to find the inertia tensor. http://www.mip.sdu.dk/~pino/inertiacyl.JPG Where the rotational axis are either the x (red) or y (green). I know that the inertia tensor for a cylinder is of the form http://www.mip.sdu.dk/~pino/inertiamoment-cylinder.jpg...

Homework Statement Compute the moment of inertia tensor I with respect to the origin for a cuboid of constant mass density whose edges (of lengths a, b, c) are along the x,y,z-axes, with one corner at the origin. The Attempt at a Solution I get I = M \left( \begin{array}{ccc}...

I need to find the inertia tensor for a uniform thin hollow cone,spinning about its ponted end. When the cone is solid then everything goes very smoothly by using cylindrical polar coordinates. But how should I find if it is a hollow cone. To be able to write the density of the cone I have...

I have just started learning about inertia tensors and am trying to do the problem in the attached document. I'm not sure how to calculate the moment of inertia about each axis. I would appreciate it if anyone could explain to me how it is done.

I'm trying to write a quick and dirty computer simulation for 3D rotational dynamics. This is the first time I've ever seen the sort of physics needed for doing this, so please bear with me. I've decided that I don't need a huge amount of accuracy in the final simulation, so I was hoping to...