Question

If $l_{A}$ is the moment of inertia of a mass distribution of total mass $M$ with respect to an axis $A$ through the center of gravity, sbow that its moment of inertia $l_{B}$ with respect to en exis $B$, which is parallel to $A$ and has the distance $k$ from it, is $$l_{B}=I_{A}+k^{2} M$$

Name: Problem 28, Chapter 10: Advanced Engineering Mathematics
Uploaded: 2022-02-04T07:16:32-08:00
Duration: 2 min 17 s
Channel: Manik Pulyani
Description: If lA is the moment of inertia of a mass distribution of total mass M with respect to an axis A through the center of gravity, sbow that its moment of inertia lB with respect to en exis B, which is parallel to A and has the distance k from it, is lB=IA+k^2 M

    If $l_{A}$ is the moment of inertia of a mass distribution of total mass $M$ with respect to an axis $A$ through the center of gravity, sbow that its moment of inertia $l_{B}$ with respect to en exis $B$, which is parallel to $A$ and has the distance $k$ from it, is $$l_{B}=I_{A}+k^{2} M$$

Advanced Engineering Mathematics

Erwin Kreyszig 9th Edition

Chapter 10, Problem 28

Instant Answer

Solved by Expert Manik Pulyani

02/04/2022

Step 1

We know that $r'^{2} = r^{2} + k^{2}$, where $k$ is the distance between the two axes. Show more…

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If $l_{A}$ is the moment of inertia of a mass distribution of total mass $M$ with respect to an axis $A$ through the center of gravity, sbow that its moment of inertia $l_{B}$ with respect to en exis $B$, which is parallel to $A$ and has the distance $k$ from it, is $$l_{B}=I_{A}+k^{2} M$$

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Key Concepts

Moment of Inertia

This concept measures an object’s resistance to changes in its rotation about an axis, and is quantitatively defined by the integral of the squared distance of each mass element from the axis times its mass. It is a fundamental quantity in rotational dynamics and serves as an analog of mass in linear motion.

Parallel Axis Theorem

This theorem provides a method to calculate the moment of inertia of a body about any axis parallel to an axis through the center of mass. It states that the moment of inertia about the new axis is equal to the moment of inertia about the center of mass axis plus the product of the total mass and the square of the distance between the two axes. This key result simplifies computations in rotational dynamics when dealing with shifted axes.

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