Moment of Inertia Calculation for Conic Disc with Hole in Center

AI Thread Summary
To calculate the moment of inertia for a conic disc with a hole in the center, treat the object as a series of concentric rings. Each mass element contributes to the moment of inertia as r^2 dm, where dm can be expressed in terms of the radius r and the density of the material. Setting up the integral involves integrating these contributions across the entire volume of the conic disc. The discussion emphasizes the importance of understanding the geometry and density distribution to accurately perform the calculations. This approach provides a systematic way to derive the moment of inertia for complex shapes.
CBrandi
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Hi everybody.
I'm a newbie here.
I'm a Physics student at University of São Paulo in Brazil (I'm in 1st year) and find this forum was a very nice surprise for me. I think this is the best thing about Physics in all web and I would like give all of you my congratulations.
Well, my doubt is about Moment of Inertia.
I need calculate the moment of inertia for a conic disc with a hole in the center according the figure below. I made several searches on Internet and didn't find nothing about this.
The diametral section of the ring is like following:
http://img178.imageshack.us/img178/7999/discocnico013ai.jpg
Thank you very much.
 
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set up the integral

Realize that the contribution of a given mass element to the moment of inertia is r^2 dm. Hint: Treat the object as composed of a set of concentric rings. Write "dm" for these rings as a function of r and the density. Integrate!
 
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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