On January 2nd:

 1492  The Emirate of Granada Falls, Completing the Reconquista

On January 2nd, 1492, the Emirate of Granada, the last Muslim stronghold in Spain, fell to the Catholic Monarchs Ferdinand II of Aragon and Isabella I of Castile. This event marked the completion of the Reconquista.

 1788  Georgia Becomes the Fourth U.S. State

Georgia, known for its peaches and rich history, became the fourth state of the United States on January 2nd, 1788. It played a significant role in the development of the American South.

1974  President Richard Nixon Signs the Emergency Highway Energy Conservation Act

Facing an energy crisis, President Richard Nixon signed the Emergency Highway Energy Conservation Act on January 2nd, 1974. The act imposed a national speed limit and promoted energy-saving measures on highways.