Combine tomatoes, garlic, red pepper flakes, 1/4 cup oil, and 1 tsp. salt in a large bowl.
Cook cavatappi in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1 cup pasta cooking liquid, and add to tomato mixture. Stir vigorously and add pasta cooking liquid and oil as needed to fully coat. Stir in arugula and black pepper and season with salt.
Transfer pasta to a serving bowl or platter and dollop with ricotta. Serve immediately.
