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Kinematics

Problem 1.58

A solid body rotates with a constant angular velocity \(\omega_{0}\) \(=0.50 \mathrm{rad} / \mathrm{s}\) about a horizontal axis \(A B .\) At the moment \(t=0\) the axis \(A B\) starts turning about the vertical with a constant angular acceleration \(\beta_{0}=0.10 \mathrm{rad} / \mathrm{s}^{2} .\) Find the angular velocity and angular acceleration of the body after \(t=3.5 \mathrm{~s}\).

Reveal Answer
ω=ω01+(β0t/ω0)2=0.6rad/s,β=β01+ω02t2==0.2rad/s2\omega=\omega_{0} \sqrt{1+\left(\beta_{0} t / \omega_{0}\right)^{2}}=0.6 \quad \mathrm{rad} / \mathrm{s}, \boldsymbol{\beta}=\beta_{0} \sqrt{1+\omega_{0}^{2} t^{2}}==0.2 \mathrm{rad} / \mathrm{s}^{2}
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