Moment of Inertia of an object rotating about its center of mass?

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SUMMARY

The moment of inertia of a composite object consisting of a uniform rod and a uniform sphere can be calculated using the Parallel Axis Theorem. For the given problem, the rod has a mass of 6 kg and a length of 4 m, while the sphere has a mass of 30 kg and a radius of 1 m. The total moment of inertia about the center of mass is derived from the individual moments of inertia of the rod and sphere, resulting in a value of 44.6959 kg·m². This calculation incorporates both the moment of inertia of the rod and the sphere, applying the necessary equations effectively.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with the Parallel Axis Theorem
  • Knowledge of basic physics equations related to rotational motion
  • Ability to perform calculations involving mass and geometry
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  • Study the derivation of the Parallel Axis Theorem in detail
  • Explore the moment of inertia for different geometric shapes
  • Learn about composite bodies and their rotational dynamics
  • Investigate applications of moment of inertia in engineering and physics
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Moment of Inertia of an object rotating about its center of mass??

Homework Statement


An object is formed by attaching a uniform, thin rod with a mass of m = 6 kg and length L = 4 m to a uniform sphere with mass M = 30 kg and radius R = 1 m.

What is the moment of inertia of the object about an axis at the center of mass of the object and about an axis at the right edge of the sphere?

Homework Equations



Parallel Axis Theorem
I=Icm+MD^2

The Attempt at a Solution



I=Irod+Iball
I=(1/12)mL^2+(2/5)MR^2 =44.6959Please help :)
 
Last edited:
Physics news on Phys.org


Parallel Axis Theorem
I=Icm+MD^2

If it's a relevant equation, try to use it... :)
 

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