Bifilar Pendulum w/ off-centred CM, need verification for derived eq.

Thread starter ChessGM
Start date Dec 31, 2024
Tags

Center Centroid Pendulum

Dec 31, 2024

ChessGM

Homework Statement: For an essay I'm looking at the MOI about the central diameter of a composite object (2 flush concentric cylinders, the external cylinder is shorter lengthwise and can slide along the longer one) with a centre of mass that is not on the central diameter. This is done through the external cylinder, and placing it some distance from the centre, and timing its period in a bifilar pendulum.

I have an equation but I'm not sure if its correct, if anyone could take the time to come up with it and cross-reference it that would be appreciated.

Relevant Equations: The "standard" equation is 2 x pi x r x sqrt(IL/mg), but now it does not work because it assumes a centred centre of mass.

Here are some diagrams:

The mass of the rod is M, and the external cylinder is m. This is what I came up with:

Physics news on Phys.org

Dec 31, 2024

berkeman

Admin

Can you show your math work that led to that result? I'll send you a message with tips for posting math here at PF using LaTeX.

Thread 'Initial conditions for orbits around a wormhole'

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...

View full post »

Thread 'How do I solve the 3D magnetic field of a Halbach Rotor?'

Boundary conditions: The derived Dirichlet and Neumann boundary conditions In terms of the magnetic scalar potential:

View full post »

Thread 'Help to convert units of a simple formula'

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 ?

View full post »