A thin rod of length L = 1 m and mass m has a linear density X(x) = Ax5 where is the distance from the rod's left end. X(x) has units of kg/m and A = 8.77 with appropriate units that can't be displayed nicely due to Canvas limitations. Calculate the rod's moment of inertia I about an axis through x = 0 and perpendicular to the rod's length. (Hint: Evaluate the integral I = fr² dm where r = x is the distance from the axis to each element of mass dm = X(x) dx . Note: The rod's total mass mass m isn't needed but, if you would like to know it, you can find it by evaluating the integral m = fdm = f(x) dx.) I = kg. m² Record your numerical answer below, assuming three significant figures. Remember to include a "-" when necessary.

A thin rod of length L = 1 m and mass m has a linear density X(x) = Ax5 where is the distance from the rod's left end. X(x) has units of kg/m and A = 8.77 with appropriate units that can't be displayed nicely due to Canvas limitations. Calculate the rod's moment of inertia I about an axis through x = 0 and perpendicular to the rod's length. (Hint: Evaluate the integral I = fr² dm where r = x is the distance from the axis to each element of mass dm = X(x) dx . Note: The rod's total mass mass m isn't needed but, if you would like to know it, you can find it by evaluating the integral m = fdm = f(x) dx.) I = kg. m² Record your numerical answer below, assuming three significant figures. Remember to include a "-" when necessary.

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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