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Kinematics

Problem 1.46

A solid body rotates about a stationary axis according to the law φ=at−\varphi=a t- −bt3,-b t^{3}, where a=6.0rad/sa=6.0 \mathrm{rad} / \mathrm{s} and b=2.0b=2.0 rad/s3\mathrm{rad} / \mathrm{s}^{3}. Find: (a) the mean values of the angular velocity and angular acceleration averaged over the time interval between t=0t=0 and the complete stop; (b) the angular acceleration at the moment when the body stops.

Reveal Answer
 (a) ⟨ω⟩=2a/3=4rad/s,⟨β⟩=3ab=6rad/s2, (b) β==23ab=12rad/s2\text { (a) }\langle\omega\rangle=2 a / 3=4 \mathrm{rad} / \mathrm{s}, \langle\beta\rangle=\sqrt{3 a b}=6 \mathrm{rad} / \mathrm{s}^{2}, \text { (b) } \beta= =2 \sqrt{3 a b}=12 \mathrm{rad} / \mathrm{s}^{2}
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