Rotational Inertia of Square Homework

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SUMMARY

The discussion focuses on calculating the rotational inertia of a rigid body formed by four identical particles, each with a mass of 0.351 kg, positioned at the vertices of a 3.50 m x 3.50 m square. The calculations involve using the formula I = mr² and I = Icom + Mh² for three different axes of rotation. The first axis passes through the midpoints of opposite sides, the second is perpendicular to the plane through the midpoint of one side, and the third passes through two diagonally opposite particles. The participants confirm the calculations for axes (a) and (c) while suggesting a reevaluation for axis (b).

PREREQUISITES
  • Understanding of rotational inertia and its significance in physics
  • Familiarity with the formula I = mr² for point masses
  • Knowledge of the concept of center of mass (Icom) and its application
  • Basic geometry of squares and diagonal calculations
NEXT STEPS
  • Review the derivation and application of the parallel axis theorem in rotational dynamics
  • Explore examples of calculating rotational inertia for various shapes and mass distributions
  • Learn about the significance of rotational inertia in real-world applications, such as engineering and mechanics
  • Investigate the effects of mass distribution on the rotational inertia of composite bodies
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators seeking to enhance their understanding of rotational inertia calculations.

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Homework Statement



Four identical particles of mass 0.351 kg each are placed at the vertices of a 3.50 m x 3.50 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


I = mr^2
I = Icom + Mh^2

The Attempt at a Solution


a) I think you would do I = mr^2 + mr^2
so, I = 2(.351)(3.5/2)^2 + 2(.351)(3.5/2)^2

b) I = .351(3.5/2)^2 + .351(3.5/2)^2 + 2(.351)(3.5)^2

c) Since the diagonal of the square is 4.95m
I = .351(4.95/2)^2 +.351(4.95/2)^2

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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hi mmiller9913! :smile:

(try using the X2 icon just above the Reply box :wink:)
mmiller9913 said:
b) I = .351(3.5/2)^2 + .351(3.5/2)^2 + 2(.351)(3.5)^2

(a) and (c) are fine :smile:

try (b) again​
 

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