How Does Theta Affect Particle Speed on an Accelerating Sphere?

quantum brain
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a particle is kept on the top of a smooth sphere of radius r.the sphere is provided an acceleration a which is a constant.find the speed of the particle as a function of theta the angle it slides from the sphere
 
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Hi quantum brain! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
please post a detailed solution
 
quantum brain said:
please post a detailed solution

:smile: :smile:

that's not the way it works

… please read the forum guidelines! :smile:
 
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 ?
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