The age of imperialism fell right on the coattails of the industrial revolution. what is the
connection between the two?

The industrial revolution, or the First and Second industrial revolutions that happened during 18th and 19th centuries, are directly connected to the Age of Imperialism: new technology demanded new raw materials to feed newly existent ways of generating power. It was the process of accelerated industrialization the origin of the need for new raw materials and consumer markets.

The First Industrial Revolution (second half of the 1700s) happened mostly on the industry. Its most radical transformation was due to the steam engine that increased production, changed the dynamics between the city and the countryside and the division of labor.

The Second Industrial Revolution was greater in terms of changes in the daily life. It was during the 1800s that happened main breakthroughs that lead to widespread use of electricity, for example. It made transports and communications faster, increasing communication and connectivity in certain parts of the world like a few European countries (mainly England) and the U.S.

To the rest of the world these revolutions meant a violent form of "connectivity". Industrialized countries now needed many natural goods they didn't have enough in their territory. Several countries were invaded and colonized and had their natural goods stolen and/or overtly explored in order to support the economic changes in Europe and the U.S., besides serving as consumer markets.