## Engineering Mechanics: Statics & Dynamics (14th Edition)

$\theta=5443rev$ $\omega=740rad/s$ $\alpha=8rad/s^2$
We can determine the required number of revolutions, the angular velocity, and the angular acceleration as follows: $\theta=4t^2+20t$ We plug in the known values to obtain: $\theta=4(90)^2+20(90)$ This simplifies to: $\theta=34200rad$ Now we can find the number of revolutions as $\theta=(34200rad)(\frac{1rev}{2\pi rad})=5443rev$ The angular velocity is given as $\omega=\frac{d\theta}{dt}$ $\omega=20+8t=20+8(90)=740rad/s$ and $\alpha=\frac{d\omega}{dt}=8rad/s^2$