The most common kind of radiation is sunlight, and the most common cause of injury from radiation is a sunburn. Just like radioactivity from a nuclear explosion, radiation from the sun can damage the DNA of your cells. Later the same day, or the next day, your skin may be red and sore. Years later, the same damage increases your chances of getting skin cancer.
One project you might do would be to test different brands of sunscreen on a sunny day. Which ones work better? Do the stronger or more expensive ones really do a better job? Do some research to find out how sunscreen works.
Bibliography and further reading about nuclear physics: