Find the rotational inertia of a rod about a pivot

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SUMMARY

The rotational inertia of a rod about a pivot located at a distance of L/3 from the left end can be calculated using the parallel-axis theorem. The moment of inertia for a rod about its center is (1/12)ML², and for a pivot at the end, it is (1/3)ML². By applying the parallel-axis theorem, the rotational inertia can be determined as I = I_center + Md², where d is the distance from the center to the pivot point.

PREREQUISITES
  • Understanding of rotational inertia and its significance in physics
  • Familiarity with the parallel-axis theorem
  • Basic knowledge of moment of inertia calculations
  • Concept of pivot points in rotational motion
NEXT STEPS
  • Study the derivation of the parallel-axis theorem in detail
  • Explore examples of calculating moment of inertia for various shapes
  • Learn about the implications of rotational inertia in real-world applications
  • Investigate the effects of friction on rotational motion and inertia
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking for practical examples of rotational inertia calculations.

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Homework Statement



i need to find the rotational inertia of a rod about a pivot. The rod is of mass M and length L and is attached to a pivot of negligible friction located at a distance of L/3 from the left end of the rod.

Homework Equations





The Attempt at a Solution



i know that if the pivot were in the center it would be (1/12)ML and if the pivot were on the end it would be (1/3)ML, but i don't know how to find it at (L/3). can anyone help me? id really appreciate it! thanks.
 
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Try the parallel-axis theorem.
 
thanks, ill try it!
 

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