Final answer:
To determine the moment of inertia of the assembly about an axis through point 0 and perpendicular to the page, calculate the moment of inertia of each object in the assembly using the formula I = m*r^2, where m is the mass of the object and r is the distance from the axis of rotation. Convert the specific weight of the material to mass by dividing by the acceleration due to gravity. Add up the moments of inertia of all the objects in the assembly to find the total moment of inertia.
Step-by-step explanation:
The moment of inertia of an assembly is the measure of its resistance to rotational motion. To determine the moment of inertia of the assembly about an axis through point 0 and perpendicular to the page, we need to consider the individual moment of inertia of each object in the assembly and add them up. The moment of inertia of an object can be calculated using the formula I = m*r^2, where m is the mass of the object and r is the distance from the axis of rotation.
Given that the material has a specific weight of gamma = 90 lb/cuft, we can convert the weight to mass by dividing by the acceleration due to gravity. The specific weight is equal to the product of the density and the acceleration due to gravity. Therefore, the density of the material is gamma/g, where g is the acceleration due to gravity. We can then calculate the mass of each object in the assembly using the density and volume.
Once we have the mass and distance from the axis of rotation for each object, we can calculate the moment of inertia of each object using the formula I = m*r^2. Finally, we add up the moments of inertia of all the objects in the assembly to find the total moment of inertia.