Maya Angelou's I Know Why The Caged Bird Sings. I am confused about character analysis homework. I need to describe a dynamic and static character. I was thinking I could use her mother as a static character, would that be right? If I used her brother, how does his interactions enhance and deepen the understanding of this book? He's in her life all the time, so I find it hard to pin point

The difference between static and dynamic is largely the extent of change and growth. Dynamic characters develop in the course of the time period covered in the work. A static character is also usually flat, without nuance, more like a stereotype than an actual person.
The most dynamic characters are Maya/Ritie and Bailey, as they grow and change considerably. In part this is because Angelou is tracing their paths from child to adult but it also relates to the insights they gain about themselves, their families, and the way the world works.
Mama is dynamic in terms of personality but static in terms of growth. As Maya largely views her through a child's eyes, she seems complete and unchanging; those are qualities a child needs to believe in.
Vivian seems static for much of the book, but is shown as dynamic when she changes her attitude toward motherhood and responsibility.
The other men tend to be static. Her father does not change his ways. Uncle Willie similarly does not develop.