Question

Determine the moment of inertia of a cylinder of radius 0.48 m, height 0.82 m and density (1.54 − 0.77 r + 0.212 r² ) kg/m³ about the center. answer in units of kg/m² .

Answer 1

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.