Question

Point-masses $m_{i}$ are located on the $x$ -axis as shown. Find the moment $M$ of the system about the origin and the center of $\operatorname{mass} \bar{x}$

Name: Problem 22, Chapter 8: Calculus: Early Transcendentals, Metric Edition
Uploaded: 2025-10-14T22:37:32-08:00
Duration: 1 min 26 s
Channel: James Kiss
Description: Point-masses mi are located on the x -axis as shown. Find the moment M of the system about the origin and the center of mass x̅

   Point-masses $m_{i}$ are located on the $x$ -axis as shown. Find the moment $M$ of the system about the origin and the center of $\operatorname{mass} \bar{x}$

Calculus: Early Transcendentals, Metric Edition

James Stewart,… 9th Edition

Chapter 8, Problem 22

Instant Answer

Solved by Expert James Kiss

10/14/2025

Step 1

The moment of a point-mass is given by the product of its mass and its distance from the origin. So, we have: - Moment of $m_1$: $M_1 = m_1 \cdot x_1$ - Moment of $m_2$: $M_2 = m_2 \cdot x_2$ - Moment of $m_3$: $M_3 = m_3 \cdot x_3$ Show more…

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Point-masses $m_{i}$ are located on the $x$ -axis as shown. Find the moment $M$ of the system about the origin and the center of $\operatorname{mass} \bar{x}$

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Key Concepts

Moment of a System

The moment of a system of point masses about a specific point is determined by summing the products of each mass with its distance from that point. This concept is crucial for understanding how forces cause rotational effects or torques, and it plays a central role in analyzing equilibrium and dynamics in mechanics.

Center of Mass

The center of mass is the point where the total mass of a system can be thought as being concentrated. It is calculated as the weighted average of the positions of all the masses, with the masses themselves serving as the weights. This concept is fundamental in simplifying the analysis of systems by reducing them to a single point mass that behaves as if all the mass were concentrated there.

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