Final answer:
The moment of inertia of a thin uniform right triangle rotating about a side of length h is found using the formula (1/6) * m * h^2 and adjusting with the parallel axis theorem if needed.
Step-by-step explanation:
The question asks for the moment of inertia of a metal sign, which is a thin, uniform right triangle, for rotation about the side of length h. The moment of inertia (I) for such a shape about its base can be calculated using the formula I = (1/6) * mass (m) * height2 (h2), assuming the axis of rotation is at the base. If the axis of rotation is at the height (side h), we need to use the parallel axis theorem to adjust this: Inew = Ibase + m * (b/2)2, where Ibase is the moment of inertia about the base, and b is the base length of the triangle.