1. **Problem Statement:** Determine the moment of inertia of the Android logo about the y-axis. 2. **Understanding Moment of Inertia:** The moment of inertia $I_y$ about the y-axis for a planar object is given by the integral: $$I_y = \int (x^2) \, dm$$ where $x$ is the distance from the y-axis to the mass element $dm$. 3. **Approach:** To find $I_y$ for the Android logo, we need its mass distribution and geometry. Since the logo is a composite shape, we can approximate it by dividing it into simpler shapes (rectangles, circles, etc.), find each shape's moment of inertia about the y-axis, and then use the parallel axis theorem if needed. 4. **Formulae for Basic Shapes:** - Rectangle about y-axis through its center: $$I_y = \frac{1}{12} m (h^2)$$ where $h$ is the height (distance along x-axis). - Circle about y-axis through its center: $$I_y = \frac{1}{4} m r^2$$ 5. **Steps:** - Identify and measure dimensions of each component of the Android logo. - Calculate each component's moment of inertia about its own centroidal y-axis. - Use the parallel axis theorem to shift to the logo's y-axis if necessary: $$I = I_{centroid} + md^2$$ where $d$ is the distance between the component's centroid and the y-axis. - Sum all components' moments of inertia to get total $I_y$. 6. **Final Answer:** Without exact dimensions and mass distribution, the moment of inertia cannot be numerically computed here. The method above outlines how to calculate $I_y$ once the logo's geometry and mass are known.