All Problems

Kinematics

Problem 1.49

A solid body rotates about a stationary axis so that its angular velocity depends on the rotation angle \(\varphi\) as \(\omega=\omega_{0}-a \varphi,\) where \(\omega_{0}\) and \(a\) are positive constants. At the moment \(t=0\) the angle \(\varphi=0\). Find the time dependence of (a) the rotation angle; (b) the angular velocity.

Reveal Answer
 (a) φ=(1−e−at); (b) ω=ω0e−at\text { (a) } \varphi=\left(1-\mathrm{e}^{-a t}\right); \text { (b) } \omega=\omega_{0} \mathrm{e}^{-a t}
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