What is the Angular Momentum of the Earth Due to its Rotation?

AI Thread Summary
The discussion focuses on calculating the angular momentum of the Earth due to its rotation. The user initially calculated the moment of inertia incorrectly using the formula for a particle instead of the correct formula for a solid sphere, which is I = 2/5 m r^2. They arrived at an incorrect angular momentum value of 1.77*10^34. Other participants pointed out the error and noted that physics textbooks typically provide tables of moment of inertia for various shapes. The conversation highlights the importance of using the correct formulas in physics calculations.
vpea
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I'm stuck on the second part of a problem and can't seem to get the right answer:

Calculate the magnitude of the angular momentum of the Earth due to its rotation around an axis through the north and south poles. Treat the Earth as a uniform sphere of radius 6.38*10^6 that makes one revolution in 24.0 hours. (m=5.97*10^24)

I got the answer 1.77*10^34 but it's wrong :(
 
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Show your work. Explain how you got your answer.
 
I found the moment of Inertia (mr^2) to be = 2.43*10^38. Then found the angular velocity to be (2pi)/(24*60*60). Using the equation I=m*r^2, I got 1.77*10^34
 
vpea said:
Using the equation I=m*r^2...
That's the moment of inertial of a particle, not a solid sphere about its center. The one you want is I = 2/5 m r^2.
 
Thanks for that! I tried looking on the internet for the moment of Inertia of the Earth and was getting all sorts of weird numbers no wonder it wasn't working.
 
vpea said:
I tried looking on the internet for the moment of Inertia of the earth

Every "General Physics" textbook I've ever seen has a table of formulas for moment of inertia of various shapes of objects. What kind of a course are you taking?
 
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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