Answer
$\theta=5443rev$
$\omega=740rad/s$
$\alpha=8rad/s^2$
Work Step by Step
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 $\alpha=\frac{d\omega}{dt}=8rad/s^2$
