Consider a "round" rigid body with moment of inertia I = BMR², where M is the body's mass, R is thebody's radius, and B is a constant depending on the type of the body.Rigid BodyUniform hoopUniform solid cylinderUniform spherical shellUniform solid sphere11/22/3k2/5The center of the "round" rigid body is attached to a spring of force constant k, and then the body ismade to roll without slipping on a rough horizontal surface. Due to the spring, it is expected the body willoscillate by rolling back and forth from its resting position.A. (6 Points) Determine the angular frequency and the period for small oscillations of the round rigidbody. Express your answer in terms of B.

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Answered: Consider a "round" rigid body with…

Consider a "round" rigid body with moment of inertia I = BMR?, where M is the body's mass, R is the body's radius, and B is a constant depending on the type of the body.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

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Consider a "round" rigid body with moment of inertia I = BMR², where M is the body's mass, R is the
body's radius, and B is a constant depending on the type of the body.
Rigid Body
Uniform hoop
Uniform solid cylinder
Uniform spherical shell
Uniform solid sphere
1
1/2
2/3
k
2/5
The center of the "round" rigid body is attached to a spring of force constant k, and then the body is
made to roll without slipping on a rough horizontal surface. Due to the spring, it is expected the body will
oscillate by rolling back and forth from its resting position.
A. (6 Points) Determine the angular frequency and the period for small oscillations of the round rigid
body. Express your answer in terms of B.

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