ω = 2000 rpm, initial angular speed.
[tex]\omega = (2000 \, \frac{rev}{min} )*(2 \pi \, \frac{rad}{rev} )*( \frac{1}{60}\, \frac{min}{s} ) = 209.4395 \, \frac{rad}{s} [/tex]
t = 30 s, the time for the wheel to come to rest.
Calculate the angular deceleration, α.
w - αt = 0
(209.4395 rad/s) - (α rad/s²)*(30 s) = 0
α = 6.9813 rad/s²
The angular distance traveled, θ, is given by
ω² - 2αθ = 0
θ = ω²/(2α)
= 209.4395²/(2*6.9813)
= 3141.6 rad
The number of revolutions is
3141.6/(2π) = 500
Answer: 500 revolutions
