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If I understand correctly, you are asking if a meteor impact could (i) slow the Earth's rotation on its axis or revolution around the Sun enough to account for the 8 to 12-fold decrease in longevity of human-kind measured in Earth days/years; and (ii) cause 40 days of torrential rain, resulting in sufficient inland flooding to float a large wooden boat. An ...

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No you cannot assume that. The initial rotation is about the major axis, and it will continue to be so (in the absence of torque, and since you were already rotating about the major axis). Instead, since $\omega_2=\omega_3=0$, your equations for the evolution of the angular momentum don't require the moments of inertia to be the same.

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As drawn the disc's angular speed $\omega$ is too fast as related to the velocity of the centre of mass of the disc $v$ for the no slipping condition ($v = R \omega$, with $R$ the radius of the disc) to be satisfied. You can think if the frictional force as trying to accelerate the centre of mass whilst at the same time the frictional force applies a torque ...

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In short, you are to think of the direction of the torque as pointing along the axis of the rotation it would induce in a rigid body initially at rest. But if the conception of torque as a vector out of the page seems artificial, that's because it is. Torque is not fundamentally a quantity that is a vector but a directed plane or directed area. Such an ...

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There are probably lots of duplicates, so my apologies, but for clarity I will try a short answer, as the graphic from Wikipedia is particularly illustrative. The torque is perpendicular, ( orthogonal) to the other two vectors, so it could be the line where the hinges are located, depending on the direction of the other two forces. From Wikipedia ...

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