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As you will most possibly know, a misreading of this paper by the media caused kind of a "panic" about how the Earth's inner core had stopped or even reversed its rotation and its "apocalyptic" effects, etc. When asked, I immediately knew that it wasn't possible ---by energetic reasons, to start with, and said it. I more-or-less thought that stopping the core relative to the mantle would need immense amounts of energy "appeared out of the blue" whose application would be truly apocalyptic ---basically, destroying the Earth. Which was and is obviously impossible.

Well, now I've been challenged to "prove it" by the usual you-know-whos and I'd like to calculate how much energy would be actually needed to stop the inner core rotation relative to the mantle, and its effects on the Earth. However, last time I went to school was to attend high school. I initially thought that a simple calculation of the rotational kinetic energy needed to deccelerate the inner core to zero would be enough, but I'm now realizing that it's possibly more complex than that ---and I'd still wouldn't know how to translate the results into "Earth destruction units".

So... please, can anyone help me?

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  • $\begingroup$ The effort of stopping something from rotating usually is a net energy gain - you have to put somewhere the kinetic energy of rotation. $\endgroup$
    – fraxinus
    Commented Jan 30, 2023 at 10:40
  • $\begingroup$ Another big problem is angular momentum conservation. To lose all this angular momentum you either have to make the outer shell rotate really fast or lose some mass to space somehow. $\endgroup$ Commented Jan 30, 2023 at 12:13

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Using this Wikipedia article for numbers:

The mass of the core is about $10^{23}$ kg. The radius is $1.22 \times 10^6$m. The moment of inertia is $\tfrac 2 5 m r^2=6 \times 10^{34} \:\text{kg}\,\text{m}^2$.

The speed of rotation relative to the mantle is said to be "0.3 to 0.5 degree per year". That's $2.8 \times 10^{-10}$ radians per second.

If that speed is accurate, the energy is $\tfrac 1 2 I \omega^2=2.3\times 10^{15}$ J.

Google tells me it's $4.184\times 10^9$J per ton of TNT. So this is actually a piddling megaton of TNT -- a decent fusion weapon by modern standards.

Now, if you asked how much energy it would take to stop it relative to space -- that's a lot more fun. The Earth rotates at $7\times 10^{-5}$ rad/s. That gives $1.6 \times 10^{26}$ J. The impact that killed the dinosaurs was $4.2\times 10^{23}$ J. So this is 500 of those.

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  • $\begingroup$ I'd probably add a disclaimer that this is back-of-the-envelope math, considering OP is probably not very familiar with such calculations. $\endgroup$
    – Passer By
    Commented Jan 30, 2023 at 11:23

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