### Use of the Parallel Axis Theorem to Determine Moment of Inertia**Problem Statement:**Using the parallel axis theorem, what is the moment of inertia of the rod of mass \( m \) about the axis shown below? (Use the following as necessary: \( m \) and \( L \).)**Diagram Description:**The diagram displays a horizontal rod with a length of \( L \). The rod is horizontally aligned, and a vertical axis of rotation is shown passing through the left end of the rod. The sections along the rod are labeled as follows:- The first section from the axis to a point \( \frac{L}{3} \) from the left end.- The remaining section from the \( \frac{L}{3} \) point to the far right end, labeled \( \frac{2L}{3} \).An arrow above the rod illustrates the rotational direction about the vertical axis through the left end.**Equation:**To solve the moment of inertia \( I \) for this scenario, use the parallel axis theorem, which is given by:\[ I = I_{\text{CM}} + md^2 \]Where:- \( I_{\text{CM}} \) is the moment of inertia about the center of mass of the rod.- \( m \) is the mass of the rod.- \( d \) is the distance between the new axis and the axis through the center of mass.Generally, for a uniform rod of mass \( m \) and length \( L \), the moment of inertia about its center of mass \( I_{\text{CM}} \) is:\[ I_{\text{CM}} = \frac{1}{12}mL \]For this problem, the distance \( d \) from the center of mass to the new axis at the left end is \( \frac{L}{2} \).So, \[ d = \frac{L}{2} \]Plugging these values into the parallel axis theorem,\[ I = \frac{1}{12}mL^2 + m\left(\frac{L}{2}\right)^2 \]Simplify,\[ I = \frac{1}{12}mL^2 + m\frac{L^2}{4} \]\[ I = \frac{1}{12}mL^2 + \frac{1}{4}mL^2 \

Given Mass of Rod=m Length of rod=L

Answered: Using the parallel axis theorem, what…

Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below? (Use the following as necessary: m and L.) 2L 3 I =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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