Circular Motion

We need to determine the number of revolutions a wheel makes before coming to a stop. Here's the breakdown of the solution:
Initial angular velocity, ω0=600rev∕min
To convert to radians per second:
ω0=600×‌

2π

60

=20πrad∕s
Angular deceleration, α=−2rad∕s2
Final angular velocity, ω=0rad∕s
Find:
Number of revolutions, N
Solution:
Using the angular kinematic equation:
ω2=ω02+2αθ
Plugging in the given values:
0=(20π)2+2(−2)θ
Simplify:
0=400π2−4θ
Rearrange to solve for θ :
4θ=400π2θ=100π2
Relate θ to revolutions:
Since θ=2πN,
2πN=100π2
Solve for N :
N=‌

100π2

2π

N=50π
Assuming π≈3.14,
N=50×3.14=157