Answer
The drill rotates through $(1.80\times 10^6)^{\circ}$
Work Step by Step
We can find the angular displacement in $1.00~s$:
$\Delta \theta = \omega ~t$
$\Delta \theta = (3.14\times 10^4~rad/s)(1.00~s)$
$\Delta \theta = 3.14\times 10^4~rad$
We can express the angular displacement in degrees:
$\Delta \theta = (3.14\times 10^4~rad) \times \frac{180^{\circ}}{\pi~rad}$
$\Delta \theta = (1.80\times 10^6)^{\circ}$
The drill rotates through $(1.80\times 10^6)^{\circ}$.
