Rotational Inertia with varying axis of rotation?

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SUMMARY

The discussion focuses on calculating the rotational inertia of a rigid body consisting of four identical particles, each with a mass of 0.475 kg, arranged at the vertices of a 1.73 m x 1.73 m square. The initial calculation for the rotational inertia about an axis through the midpoints of opposite sides yields a value of 0.948 kg*m² using the formula Icom = (1/12)M(a² + b²). The user seeks guidance on how to compute the rotational inertia for two additional axes: one perpendicular to the plane of the square and one passing through diagonally opposite particles.

PREREQUISITES
  • Understanding of rotational inertia and its significance in physics.
  • Familiarity with the formula Icom = (1/12)M(a² + b²) for calculating rotational inertia.
  • Basic knowledge of geometry, particularly regarding squares and diagonals.
  • Ability to perform calculations involving mass and distance in physics contexts.
NEXT STEPS
  • Learn how to calculate rotational inertia about an axis perpendicular to the plane of a square.
  • Study the method for determining rotational inertia through diagonally opposite particles.
  • Explore the parallel axis theorem for additional insights into rotational inertia calculations.
  • Review examples of rotational inertia calculations for various geometric configurations.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators seeking to enhance their understanding of rotational inertia concepts.

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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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bump, can anyone lend any advice to this question? :-\
 

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