In what respects did the roots of the industrial revolution lie within europe? in what ways did that transformation have global roots?

The European societies were highly divided and competed with each other more than any other place on Earth. That's why they favored innovation and who ever managed to discover something new they managed to cash in on it a lot and find a way  to further develop it because it would give them an edge over their opponents.

The global roots can be explained in two ways. One is that the 1500 and later Europe was a global trading hub and people from all over the world traveled there and shared their ideas and resources and similar things and since they came from all over the world, many of European innovations were inspired by people who were not originally European.

The other way is that European countries had colonies all over the world. Without the colonies, it would've been impossible to compete with others since they needed resources. Resources from all around the world, mostly the Americas, helped Europe become the power it was and develop even further.