A circular hole of radius R/4 is cut from a uniform circular disc of radius R at a distance R/2 from the center of the disc as shown in figure. If the mass of the given disc is M, (a)find the moment of inertia of this dise about an axis passing through its center and normal to its plane, (b) find the moment of inertia of the dise about an axis passing through cencer of the hole and normal to its plane. R/2 (moment of inertia of a uniform cireular dise about an axis passing through its center is 1/2 MR") R4

A circular hole of radius R/4 is cut from a uniform circular disc of radius R at a distance R/2 from the center of the disc as shown in figure. If the mass of the given disc is M, (a)find the moment of inertia of this dise about an axis passing through its center and normal to its plane, (b) find the moment of inertia of the dise about an axis passing through cencer of the hole and normal to its plane. R/2 (moment of inertia of a uniform cireular dise about an axis passing through its center is 1/2 MR") R4

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.4P

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

A circular hole of radius R/4 is cut from a uniform circular dise of radius R at a distance R/2 from the center
of the disc as shown in figure. If the mass of the given disc is M, (a)find the moment of inertia of this disc
about an axis passing through its center and normal to its plane, (b) find the moment of inertia of the dise
about an axis passing through center of the hole and normal to its plane.
R/2
(moment of inertia of a uniform cireular dise about an axis passing through its center is 1/2 MR³)
R/4

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