Solved: 5154 The tendency of a solid to resist a change in rotationalmotion about an
Chapter 14, Problem 52(choose chapter or problem)
51–54 The tendency of a solid to resist a change in rotational motion about an axis is measured by its moment of inertia about that axis. If the solid occupies a region \(G\) in an \(xyz\)-coordinate system, and if its density function \(\delta(x, y, z)\) is continuous on \(G\), then the moments of inertia about the \(x\)-axis, the \(y\)-axis, and the \(z\)-axis are denoted by \(\left.\right|_{x}, I_{y '} \text { and } I_{z}\), respectively, and are defined by
\(I_{x}=\iiint_{G}\left(y^{2}+z^{2}\right) \delta(x, y, Z) d V\)
\(L_{y}=\iint_{G}\left(x^{2}+z^{2}\right) \delta(x, y, z) d V\)
\(\mathrm{L}_{\mathrm{z}}=\iiint_{G}\left(\mathrm{x}^{2}+y^{2}\right) \delta(\mathrm{x}, y, z) \mathrm{d} \mathrm{V}\)
In these exercises, find the indicated moments of inertia of the solid, assuming that it has constant density \(δ\).
\(\mathrm{I}_{\mathrm{y}} \text { for the solid cylinder } x^{2}+y^{2} \leq a^{2}, 0 \leq z \leq h \text {. }\)
Equation Transcription:
text transcription:
delta(x,y,z)
I_x, I_y,I_z
I_x = triple sum of triple integral G (y^2+z^2)delta(x,y,z)dv
I_y = triple sum of triple integral G (y^2+z^2)delta(x,y,z)dv
I_z = triple sum of triple integral G (y^2+z^2)delta(x,y,z)dv
x^2+y^2 leqa^2, 0 leq z leq h
x,y,z-axis
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer