Constant Angular Acceleration

The particle began to move from rest along a circle with a constant angular acceleration. After five cycles (n = 5), its angular velocity reached the value ω = 12 rad/s.
Calculate the magnitude of the angular acceleration ε of this motion and the time interval required for the first five cycles.

Final Answer:

ε =  2.2918 rad/s²
t =  5.236 s

Step-by-step explanation:

$$\begin{gathered} \omega =12\text{rad/s} \\ n=5 \\ \alpha =n\cdot 2\pi =5\cdot 2\cdot 3.1416\doteq 31.4159\text{rad} \\ \alpha =\frac{1}{2}\cdot \epsilon \cdot t^2 \\ \epsilon =\omega /t \\ \alpha =\frac{1}{2}\cdot \omega /t\cdot t^2 \\ \alpha =\frac{1}{2}\cdot \omega \cdot t \\ t=2\cdot \alpha /\omega =2\cdot 31.4159/12\doteq 5.236\text{s} \\ \epsilon =\omega /t=12/5.236=2.2918{\text{rad/s}}^2 \end{gathered}$$

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