A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis i

Name: Problem 63, Chapter 9: Physics
Uploaded: 2020-04-09T18:01:07-08:00
Duration: 1 min 42 s
Channel: Mike Gaerlan

step 1 Okay, so this is a conservation of angular momentum problem. We have the angular momentum before

Question

A thin rod has a length of $0.25 \mathrm{m}$ and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of $0.32 \mathrm{rad} / \mathrm{s}$ and a moment of inertia of $1.1 \times 10^{-3} \mathrm{kg} \cdot \mathrm{m}^{2} .$ A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass $=4.2 \times 10^{-3} \mathrm{kg}$ ) gets where it's going, what is the angular velocity of the rod?

   A thin rod has a length of $0.25 \mathrm{m}$ and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of $0.32 \mathrm{rad} / \mathrm{s}$ and a moment of inertia of $1.1 \times 10^{-3} \mathrm{kg} \cdot \mathrm{m}^{2} .$ A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass $=4.2 \times 10^{-3} \mathrm{kg}$ ) gets where it's going, what is the angular velocity of the rod?

Physics

John D. Cutnell,… 11th Edition

Chapter 9, Problem 63

Instant Answer

Solved by Expert Mike Gaerlan

04/09/2020

Step 1

First, we need to find the initial angular momentum of the rod. We can do this using the formula: Angular momentum (L) = Moment of inertia (I) × Angular velocity (ω) Show more…

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A thin rod has a length of $0.25 \mathrm{m}$ and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of $0.32 \mathrm{rad} / \mathrm{s}$ and a moment of inertia of $1.1 \times 10^{-3} \mathrm{kg} \cdot \mathrm{m}^{2} .$ A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass $=4.2 \times 10^{-3} \mathrm{kg}$ ) gets where it's going, what is the angular velocity of the rod?

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Key Concepts

Conservation of Angular Momentum

This principle states that if no external torques act on a system, the total angular momentum remains constant. In the context of a rotating system with internal changes (like a bug moving along the rod), any increase in the system's moment of inertia must be accompanied by a decrease in angular velocity to keep the angular momentum unchanged.

Moment of Inertia

Moment of inertia is a measure of an object’s resistance to changes in its rotation and depends on how mass is distributed relative to the axis of rotation. When additional mass moves away from the axis (as when the bug crawls outward), it increases the moment of inertia, thereby affecting the system's rotational dynamics under conservation of angular momentum.

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