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.
('ac' denotes the normal acceleration)
Buildings would be intentionally constructed along a latitude dependent critical angle. Otherwise, a large torque would manifest at their base, much like it would if we built leaning buildings in a vertical-g environment. Buildings would be north leaning in the northern hemisphere and south leaning in the southern hemisphere. Who knows, someone might build a "Vertical Tower of Pisa" to attract tourists.
Special note for mechanics students... Note how the normal acceleration points inward, yet the effect is to make us feel lighter, akin to an outward acting force. This direction confusion can be explained by Newton's Second Law, where forces and inertial terms ('ma' terms) appear on opposite sides of the equal sign. Sometimes, the term associated with normal acceleration is brought to the other side of the equation and referred to as a pseudo-force. An inward acceleration leads to an outward pseudo-force, which, in effect, reduces the normal force acting on our feet when we stand up.