Rotational Inertia with varying axis of rotation?

AI Thread Summary
The discussion focuses on calculating the rotational inertia of a square configuration of four identical particles. The total mass of the system is determined to be 1.9 kg, and the inertia for the first axis (midpoints of opposite sides) is calculated as 0.948 kg*m². The user seeks guidance on how to compute the rotational inertia for the other two specified axes: one perpendicular to the plane through the midpoint of a side and another through two diagonally opposite particles. The conversation highlights the need for assistance in applying the appropriate formulas for these different axis orientations. Understanding the rotational inertia for various axes is essential for solving the problem accurately.
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Homework Statement



Four identical particles of mass 0.475 kg each are placed at the vertices of a 1.73 m x 1.73 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the midpoints of opposite sides and lies in the plane of the square, (b) passes through the midpoint of one of the sides and is perpendicular to the plane of the square, and (c) lies in the plane of the square and passes through two diagonally opposite particles?

Homework Equations


Icom = (1/12)M(a^2 + b^2)

The Attempt at a Solution


M = 0.475 * 4 = 1.9kg
I = (1/12)M(a^2 + b^2) = (1/12)(1.9)(1.73^2 * 2) = 0.948 kg*m^2

I believe this answer would be correct for part (a), but how do I go about calculating the rotational inertia for the other two locations of the rotational axis? Any help would be greatly appreciated, thanks!
 
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