how did the U.S. became in world power between 1890-1920.?

It didn't.

It was a regional power, but not a World power. That would only come with American involvement in WWII.

During the period 1890 - 1920 the USA had an isolationist policy - that is, it would not get involved in the affairs of other countries. It's army was small, its navy small and, in 1920, its air force tiny.

However, it was a banking and manufacturing powerhouse - mostly because of the size of its internal market. This enabled American bankers and industrialists to set up operations in the other industrialised countries - ie.e Britain & France.

BTW - the British Navy was, even after it was "weakened" due to WWI, still larger than the next two smaller navies - it would maintain that ration until about 1955.

Anerica was a rising industrial power. By the late nineteenth century, the United States had become a leading global industrial power, building on new technologies (such as the telegraph and steel), an expanding railroad network, and abundant natural resources such as coal, timber, oil and farmland, to usher in the Second Industrial Revolution.

There were two important wars. The US easily defeated Spain in 1898, which unexpectedly brought a small empire, of which Puerto Rico and (and some smaller islands) became permanent possessions (as did Alaska, added by purchase in 1867, and Hawaii, which was annexed by the U.S. in 1898).

The United States late (1917) entry in World War I on the side of the Allied Powers led to a decisive Allied victory thanks to American financial, agricultural, industrial and military strength.

We should take some lessons from that era. An era when we innovated, built things and respected a man's hard work. Now we have exported our manufacturing base, don't innovate as much and we work for the banksters who are sucking this country dry like parasites.

The Great White Fleet

Teddy Roosevelt and the big stick

The Phillipines

I think because of the advancement in science and industrial fields...

WW1 weakened european navies; thus bringing in the US and Japan as naval superpowers

Magnets.

We are just awesome!