Let's calculate the moment of inertia for a rotating rod. The general definition for the moment of inertia is I = f r²dm Let's suppose we have a uniform rod of length R with mass M, then our line density is M where we have ignored the thickness of the rod to simplify the problem. Density is an intrinsic variable, meaning that it is a constant and doesn't change for varying lengths; thus we can rephrase this equation in terms of the measured infinitesimals as dm = A dr As a reminder, the r in our moment of inertia definition is the distance from the rotating axis to the mass, so rotating about the edge of rod will yield a different result than if we rotated about the middle of the rod. Let's do the latter example here and save the former as an exercise for you to do. If we rotate the rod through the center, then our integration limits become -R/2 to R/2, S+R/2 |+R/2

Let's calculate the moment of inertia for a rotating rod. The general definition for the moment of inertia is I = f r²dm Let's suppose we have a uniform rod of length R with mass M, then our line density is M where we have ignored the thickness of the rod to simplify the problem. Density is an intrinsic variable, meaning that it is a constant and doesn't change for varying lengths; thus we can rephrase this equation in terms of the measured infinitesimals as dm = A dr As a reminder, the r in our moment of inertia definition is the distance from the rotating axis to the mass, so rotating about the edge of rod will yield a different result than if we rotated about the middle of the rod. Let's do the latter example here and save the former as an exercise for you to do. If we rotate the rod through the center, then our integration limits become -R/2 to R/2, S+R/2 |+R/2

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 10.5CYU: Check Your Understanding What is the moment of inertia of a cylinder of radius R and mass m about an...

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