How Do You Calculate the Rotational Inertia of a Composite Object?

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SUMMARY

The discussion focuses on calculating the rotational inertia of a composite object consisting of a circular hoop and a square made of four thin bars. The circular hoop has a radius of 0.50 m and a mass of 3.0 kg, while each bar of the square also has a mass of 3.0 kg. The relevant equations for rotational inertia include I of point mass = mr², I of hoop = mr², and I of rod = 1/3 mr². The user struggled to combine the rotational inertia of the hoop and the rods correctly to find the total inertia about the vertical axis of rotation.

PREREQUISITES
  • Understanding of rotational inertia concepts
  • Familiarity with the equations for point mass, hoop, and rod inertia
  • Basic knowledge of composite objects in physics
  • Ability to visualize and analyze rigid body rotation
NEXT STEPS
  • Calculate the total rotational inertia of the composite object using I of hoop and I of rods
  • Explore the effects of changing mass and radius on rotational inertia
  • Learn about parallel axis theorem for composite objects
  • Investigate real-world applications of rotational inertia in engineering
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to explain composite object inertia calculations.

dari09
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Rotational Inertia Problem--PLEASE HELP!

Homework Statement



Figure 12-39 shows a rigid structure consisting of a circular hoop, of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis with a period of rotation of 1.0 s. Assuming R = 0.50 m and m = 3.0 kg, calculate the structure's rotational inertia about the axis of rotation

The figure is attached

Homework Equations



I of point mass = mr^2
I of hoop = mr^2 or .5mr^2
I of rod = 1/3 mr^2

The Attempt at a Solution



I tried to add the I of the hoop and two of the rods together (because the other two rods are parallel to the rotating axis) but nothing that I've tried really worked...
 

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http://panda.unm.edu/Courses/Price/Phys160/p27-2.pdf"
 
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