Symmetric object prove principle axis goes through CM

m0nk3y
Messages
23
Reaction score
0

Homework Statement


c) For such a "symmetric" object, prove that any axis going through the center of mass is a principal axis.


Homework Equations


mimg276.gif



The Attempt at a Solution



I am not sure how they want me to prove this. I was looking at the Displacement Axis Thm but I am not sure how to use it, or appropriate for this problem.

Thanks in advance.
 
Physics news on Phys.org
The tensor of inertial you have is a sum of that for a stick and that for a disk.
Each of these has all principal axes through the center.
 
Thank you for your reply,

Is there a way to prove this with math?
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top