Moment of inertia, Sphere. New method.

AI Thread Summary
The discussion centers on finding the moment of inertia of a solid sphere, specifically proving it as 2/5mR^2. Participants mention various methods, with one contributor noting they have identified four calculus-based approaches, including methods using disks and shells. There is curiosity about how the disk methods differ and a request for clarification on the sphere method. The conversation hints at the possibility of more experimental methods existing beyond the 18 mentioned by the professor. Overall, the thread seeks to explore and expand the understanding of calculating the moment of inertia for a sphere using diverse techniques.
jaeoos
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Q. Show the moment of inertia of sphere is 2/5mR^2
using many different methods.

My professor said he knew 18 different method.
Do you have a new idea?
Tell me anything you know. I hope one of your methods will be the 19th method.
 
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Perhaps your professor was referring to experimental methods of finding moment of inertia of a solid sphere ( I am sure there are more than 18).
The only method, by way of proof, that I know of involves calculus.
 
I have found 4 methods involving calculus.
calculus from disk(2 methods), sphere and shell.
 
Your two methods using discs, how do they vary ?
Also I would like to know your approach using a sphere .
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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