Calculus 3: Tensors (20 of 45) What is the Meaning of the OFF-Diagonal Elements?

In this video I will explain what is the meaning of the off-diagonal elements in an inertia tensor matrix.

Next video in the series can be seen at:

[etusax]

Hello Michel! I enjoy your series. I'm not sure if you still read the comments, but incase you do:

I'm banging my head on how are these torque vectors made up. What is their direction, what defines it? In an earlier section the "Torque subindex x" was paraller to the z-axis, but on this example it seems to be something totally else (if visually read). It means a torque that makes the particle rotate around the x-axis, so it still could be paraller to z-axis. And on an earlier example where the point was (1, 1, 0), the Tx and Ty vectors were drawn as opposite vectors. I don't understand how these are done at all. :(

[foxhound]

The off diagonal elements are an indication of symmetry. If there was and equal mass, on the exact opposite side, the off diagonal elements would be zero. Meaning that the angular momentum generated in the “Y” direction due to torque about the “X” axis would be zero. If I remember correctly, these motions about an axis, about which no torque has been applied, is actually called the “wobble” of the system.

[daydreams]

What is the definition you're using for torque vectors?

I feel rather confused, because I know torque as "r x F = T" where r is the position vector and F is a force vector, but in NONE of your examples I feel like this is being followed... Could you please explain your logic on those vectors?

[منوعات-تف]

Does the particle rotate around all axis at the same time if the off diagonals are non zeros ….. help

[منوعات-تف]

Do the three torques applied simultaneously?

[jerrymahone]

get out your fidget spinner. you will see that there is no torque when you move your hand forward and back or up and down. there is no torque at 90 degrees and 180 degrees. there has to be a continuous twisting motion for you to feel the torque. there is a direct correlation between spin and torque. Michael I believe wobble has to do more with spin and gravity. torque doesn't present itself until spin has decreased to the point the object can't resist gravitational attraction. at this point torque to hold the object up. until spin has decayed to the point that torque is no longer factor. as I said earlier for torque to occur there has to be a continuous twisting action against the spin. I noticed with my finger spinner torque resist me twisting the spinner and aids me in twisting it back to a 90 degree position. I hypothesize that a decaying spinning object could get a bounce off of torque causing a wobbling effect. this is because of the decaying spin.