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Elastic deformations

Problem 1.296

A thin uniform copper rod of length ll and mass mm rotates uniformly with an angular velocity ω\omega in a horizontal plane about a vertical axis passing through one of its ends. Determine the tension in the rod as a function of the distance rr from the rotation axis. Find the elongation of the rod.

Reveal Answer
 1.296. T=1/2mω2l(1−r2/l2),Δl=1/3ρω2l3/E, where ρ is  the density of copper. \begin{aligned} &\text { 1.296. } T=1 / 2 m \omega^{2} l\left(1-r^{2} / l^{2}\right), \quad \Delta l=1 / 3 \rho \omega^{2} l^{3} / E, \text { where } \rho \text { is }\\ &\text { the density of copper. } \end{aligned}
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