All Problems

Kinematics

Problem 1.49

A solid body rotates about a stationary axis so that its angular velocity depends on the rotation angle φ\varphi as ω=ω0−aφ,\omega=\omega_{0}-a \varphi, where ω0\omega_{0} and aa are positive constants. At the moment t=0t=0 the angle φ=0\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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