Moment of inertia in plane translation

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SUMMARY

The discussion focuses on calculating the moment of inertia of a disc with mass 'M' and radius 'R' about an axis perpendicular to its plane and passing through point 'O', located at a distance 'd' from the disc's center. The user seeks clarification on four scenarios: stationary disc, disc in translatory motion, disc rotating about its center of mass, and a combination of translatory and rotational motion. The parallel axis theorem is applicable for scenarios involving rotation, but the user questions its relevance for stationary and translatory cases. The moment of inertia is established as a property that can exist independently of rotation.

PREREQUISITES
  • Understanding of moment of inertia and its definition
  • Familiarity with the parallel axis theorem
  • Knowledge of translatory and rotational motion concepts
  • Basic principles of mechanics and rigid body dynamics
NEXT STEPS
  • Study the application of the parallel axis theorem in various scenarios
  • Explore the relationship between moment of inertia and angular momentum
  • Investigate the effects of translatory motion on moment of inertia
  • Learn about composite bodies and their moment of inertia calculations
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the principles of moment of inertia in both translational and rotational dynamics.

arvindsharma
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I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane of the disc and passing through point 'O'?If,
(1)Disc is stationary
(2)Disc is having translatory motion such that perpendicular distance between center of disc and point 'O' remains same?
(3) disc is rotating about an axis perpendicular to its plane and passing through its center of mass?
(4)disc have both type of motions as in part 2 and part 3?

As far as i know moment of inertia is defined for rotation only so i could not answer part 1 and part 2(can i apply parallel axis theorem for first two parts?)for part 3 i applied parallel axis theorem and got right answer.unfortunately answer for part 4 was not even given in the book.can someone help me how to solve part 1,2 and 4th.
i will be thankful.
 
Physics news on Phys.org
Moment of inertia plays the same role for rotational motion that mass plays in linear motion.
An object can have a moment of inertia without rotation just like it can have mass without translating.

The questions ask about the moment of inertia wrt a particular axis.
What are the things that have to change for the moment of inertia about this axis to change?
 

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