Long story short, the plastic and metal material itself is not becoming radioactive.
What does happen is parts of the *actual* radioactive material can rub off, brush off, scrape off, etc. and cling to the plastic or metal. This is generally called *contamination*. So now you’ve got a metal tool that also has some radioactive material on it spewing out radiation. In some cases it is possible to clean that tool or material off (decontaminate).
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