Final answer:
An increased rate of Earth's rotation would lead to shorter days, an increase in centrifugal force causing greater equatorial bulging, changes to Earth's moment of inertia, and impacts on climate patterns and modern civilization. Sidereal days would also become shorter.
Step-by-step explanation:
If the rate of Earth's rotation on its axis increased, several changes would likely occur. Foremost, the length of a day would become shorter since the Earth would be spinning faster. In terms of physics, this is related to conservation of angular momentum, which states that if an object contracts and has less moment of inertia, it spins faster. An example of this is when stars spin faster when they collapse due to their decreasing radius and therefore reduced moment of inertia.
Another consequence would be an increase in the centrifugal force experienced at the Earth's equator. This might lead to greater equatorial bulging, thereby potentially altering the shape of the planet. Such a change in shape impacts Earth's moment of inertia, which would further influence rotation dynamics. Moreover, alterations to the rotation rate could affect numerous Earth systems, including climate patterns, and could have profound effects on modern civilization.
From an astronomical standpoint, sidereal days, which are measured by the Earth's rotation relative to distant stars, would also become shorter. This is much like how the sidereal day would change if Earth moved faster in its orbit around the Sun.