To estimate the moment of inertia $I_y$ of the IOLab device, we can use the formula for the moment of inertia of a solid rectangular block rotating about its center of mass along the y-axis (perpendicular to the width and thickness). The formula for a rectangular block with mass $M$, width $w$, and thickness $t$ is:

$I_y = \frac{1}{12} M (w^2 + t^2)$

Steps:

1. Measure the width $w$ and thickness $t$ of the IOLab device (in meters).
2. Use $M = 0.2 \, \text{kg}$ as given.
3. Substitute $w$, $t$, and $M$ into the formula above.
4. Calculate $I_y$.

Assuming your values for $w$ and $t$ fall within a reasonable range, your $I_y$ should indeed be less than $0.0002 \, \text{kg} \cdot \text{m}^2$.

Would you like further guidance on measurement techniques, or any clarification on the formula? Here are some questions to deepen understanding:

1. What effect does changing the width $w$ have on $I_y$?
2. Why does the formula use $\frac{1}{12}$ as a coefficient?
3. What would happen to $I_y$ if the mass distribution of the block was uneven?
4. How would you calculate the moment of inertia if the device had different material densities across its width?
5. Why does the moment of inertia depend on the square of the dimensions $w$ and $t$?

Tip: Measuring with high precision is important because small changes in width or thickness can significantly affect $I_y$.