Why is the following situation impossible? A meteoroid strikes the earth directl

Question

Why is the following situation impossible?

A meteoroid strikes the earth directly on the equator. At the time it lands, it is traveling exactly vertical and downwards. Due to the impact, the time for earth to rotate once increase by 0.5 s, so the day is 0.5 s longer, undetectable to laypersons. After the impact, the people on earth ignore the extra half-second and life goes on as normal.

I'm assuming what the issue is here is that the meteoroid would have to be extremely large in order to make a 1/2 second change. I just don't know how to find the size of the meteor.

Explanation / Answer

Well, if the meteor struck at an appropriate angle, one could approximate the torque exerted on the earth about its axis by multiplying the force needed to stop the asteroid by the distance away from the axis that the force was applied, then use the moment of inertia of earth to calculate what sort of angular acceleration the earth went under the split-second the meteor was decelerating. However, since the asteroid impacted the equator, directly vertical and downwards, the force would pass through the center of the earth and therefore could cause no torque about the axis due to passing through it, and no matter how big it was could not affect the rotation of earth (assuming earths center of gravity is somewhere near its physical center).

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