Angular rotation

The drill used by the most dentists today is powered by a small air-turbine that can operate at angular speeds of 350000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in 2.0 s.

Part A: Find the angular acceleration produced by the drill, assuming it to be constant. Express your answer using two significant figures

Step 1: 

ω = 350000 rpm (revolution per minute), but in SI unit is rad/s so we have to convert to rad/s. 
1 rev = 2π rad
1 min = 60 s
So we get ω =  (350000 rev)*( 2π rad/rev)*(1/60 s/m) =36651.9 rad/s
Step 2:
the drill starts at a rest so we get initial angular speed: ω0 = 0 rad/s
Time to exceed the angular speeds of jet engines: Δt = 2 s
what is angular acceleration: α = ?
Step 3:
ω = ω0 + α*t
<=> ω = α*t
=> α = ω/t = 36651.9/2 = 18326 rad/s^2 = 18326/(2π ) rad*rev/rad/s^2 = 2916.7 rev/s^2
using two significant figures so: α =2900 rev/s^2

Part B:    How many revolutions does the drill bit make as it comes up to speed? Express your answer using two significant figures

Δθ = (1/2)*α*t^2 + ω0*t = 1/2*α*t^2 = 1/2*2900*2^2 = 5800 rev=