Friday, February 7, 2014

What if the Earth Spun Faster?

Yes, these are the kinds of questions that sail through my brain.  Deal with it.

By this question, I do not mean, "What if some orbital event occurred, say, a collision with a large asteroid, and it imparted a significant angular impulse on our planet?"  After all, if such an event occurred, our new spin rate would be of little concern, because if anyone did survive, they'd be preoccupied with the task of finding their next meal.

My question is more along the lines of, "What if, in the Earth's early formation, the net angular momentum of its particles about the center of spin had been a lot greater?"  How would life be different?

To perform analyses, let us pretend that the spin rate were ten times faster, resulting in a 2.4 hour day.

How would such a change have impacted biological evolution on this planet?  If nothing else, our sleep cycles would be different.  There would be far worse and more frequent hurricanes.  And, we'd need to invent more holidays to fill the 3,652 days of the year.

My real interest, however, is the impact that such a change in angular velocity would have on the mechanics of life.

At present, the Earth's angular rotation leads to a normal acceleration at the surface of the equator of about 0.0337 m/s/s.  This acceleration makes the normal force on the bottom of our feet when we stand on the equator slightly less than our weight force.  It brings our apparent weight down by about 0.4%, which is not really noticeable.  This is because the surface gravity is about 9.8 m/s/s, and clearly dominates any rotational effects.

If we stand on the geometric north or south pole, we experience no such effect, as we are standing on the axis of spin, and the radial arm is zero.  Consider, however, the mechanics of standing at an intermediate latitude, as most of us do...

In Montreal, Quebec, where I reside, the latitude is about 45 degrees.  The magnitude of the normal acceleration felt here is actually 71% of that felt along the equator, so 0.0267 m/s/s.  The interesting thing is that this acceleration does not point parallel to the gravitational field here as it does on the equator.

Fig. 1: Gravitation and acceleration vectors in Montreal
('ac' denotes the normal acceleration)