Final answer:
To determine the moment of inertia of a cylinder, use the formula I = (1/2) * m * r^2 + (1/12) * m * h^2, where m is the mass, r is the radius, and h is the height of the cylinder. Find the mass by integrating the given density equation. Then substitute the mass into the moment of inertia formula.
Step-by-step explanation:
The moment of inertia of a cylinder can be calculated using the formula:
I = (1/2) * m * r^2 + (1/12) * m * h^2
Where:
- I is the moment of inertia
- m is the mass of the cylinder
- r is the radius of the cylinder
- h is the height of the cylinder
First, we need to find the mass of the cylinder by integrating the given density equation:
m = ∫(1.54 - 0.77r + 0.212r^2)dr
Once we have the mass, we can substitute it into the moment of inertia formula to find the moment of inertia of the cylinder.