To determine the factor by which the meteorite's impact affects the Earth's rotational frequency, we can use the principle of conservation of angular momentum. Here are the steps:

1. Known Values:

   • Mass of meteorite, $m = 6.0 \times 10^{10} \, \text{kg}$
   • Speed of meteorite, $v = 2.2 \times 10^4 \, \text{m/s}$
   • Radius of Earth, $R = 6.37 \times 10^6 \, \text{m}$
   • Rotational frequency of Earth (before impact), $f_{\text{initial}} = 1 \, \text{rev/day}$

2. Angular Momentum of the Earth:

   • Earth's moment of inertia, $I_{\text{Earth}} = \frac{2}{5} M_{\text{Earth}} R^2$, but for rotational motion at the equator, we approximate it with $I_{\text{Earth}} = M_{\text{Earth}} R^2$.
   • Angular velocity of Earth before impact, $\omega_{\text{initial}} = \frac{2\pi}{T}$, where $T = 86400 \, \text{s}$ (1 day).

3. Angular Momentum of the Meteorite: Since it strikes the Earth tangentially at the equator, the meteorite's angular momentum just before impact is: $L_{\text{meteorite}} = m \cdot v \cdot R$

4. Conservation of Angular Momentum: After the impact, the system’s total angular momentum remains conserved: $I_{\text{Earth}} \cdot \omega_{\text{initial}} + m \cdot v \cdot R = (I_{\text{Earth}} + m \cdot R^2) \cdot \omega_{\text{final}}$ Solving for $\omega_{\text{final}}$ and finding the change in frequency (since $f = \frac{\omega}{2\pi}$), we get the factor change.

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Let's proceed with the calculations:The factor by which the Earth's rotational frequency changes due to the meteorite's impact is approximately $1.0$, meaning the effect is negligible to two significant figures.

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Related Questions

1. How would the impact of a larger meteorite change the rotational frequency?
2. What would happen to Earth's rotation if the meteorite struck at the poles instead?
3. How does the mass distribution of Earth affect rotational stability?
4. How does angular momentum influence the conservation of Earth's rotation?
5. What would be the energy release of such a high-velocity impact?

Tip:

In rotational motion problems, always check if angular momentum conservation applies—it's a powerful tool for simplifying complex interactions.