A wheel is rotating at 20rad/s is brought to rest by a constant torque in 4 seconds. If the moment of inertia of the wheel is 0.3 kgm^2, what is the angle rotated by the wheel in the first 2 seconds?

Given conditions can be written as, 

ω1 = 20 rad/s
I = 0.3 kgm2
t = 4 s

∵ ω2 = ω11
-  αt

⇒ 0 = 20 - α × 4

⇒ 4α = 20

⇒ α = 204

∴ α = 5 rad/s2

Now,
for t = 2 s

∵ θ = ω1xt + 1/2(αt²)

⇒ θ = 20 x 2 + 1/2(5 x 2²)

⇒ θ = 40 - 10

∴ θ = 30 rad

angle by which it rotates is 30 rad