A machine part rotates at an angular speed of $0\mathrm{.}33$ rad$/$s; its speed is then increased to $2\mathrm{.}6$ rad$/$s at an angular acceleration of $0\mathrm{.}60$ rad$/$s$2.$

$($a$)$ Find the angle through which the part rotates before reaching this final speed.

rad

$($b$)$ In general, if both the initial and final angular speed are doubled at the same angular acceleration, by what factor is the angular displacement changed? Why? Hint: Look at the form of the equation

$2=$i$2+2.$