Moment of inertia of the Earth: I=8.04e37

Angular velocity, with sidereal rotation period of 23.93 hours: ω0=2π/(23.93 × 3600)

Angular velocity, with sidereal rotation period of 23.93 hours plus one second: ω1=2π/(23.93 × 3600 + 1)

Rotational energy difference: .5 × I × ω0 ** 2 - .5 × I × ω1 ** 2 ≈ 4.96e+24 J

For comparison, according to https://ourworldindata.org/energy-production-consumption the total amount of energy consumed on Earth in 2023 was 180E3 TWh i.e. 6.48e+20 J

Slowing down the Earth by one second would be equivalent to 7661 times this amount.

The earth moment of inertia is about I=8e37 kg m2 [2]

The energy extracted by a slowdown of angular speed from wa to wb would be 1/2 I(wa2-wb2).

Approx wa=2pi/86400 and wb=2pi/86401. Energy extracted: 4.9e24J=4.9e12TJ.

We would have energy for about 12 billion years.

If I double check with Kagi's assistant with Claude 3.7 (I'm in my phone and I could easily have made an error) it starts with my exact reasoning and figures but messes up final numbers (so close!!!) to give a total of 40 billion years, which nevertheless is the correct order of magnitude.

[1] https://en.m.wikipedia.org/wiki/World_energy_supply_and_cons...

[2] https://scienceworld.wolfram.com/physics/MomentofInertiaEart...