Starting from rest, a wheel is uniformly accelerated at 4 rad/s ^2 for 10 seconds. Subsequently, it rotates uniformly for the next 10 seconds, and is finally brought to rest over the following 10 seconds. Determine the total angle rotated by the wheel.

Step-by-step solution

The motion of the wheel can be divided into three phases. In the first phase, the wheel starts from rest and accelerates uniformly. Initial angular velocity, ₀ = 0 Angular acceleration, ₁ = 4 rad/s ^2 Time, t₁ = 10 s Angle rotated, ₁ = ₀ t₁ + 1 2 ₁ t₁^2 = 0 + 1 2 4 (10)^2 = 200 rad Angular velocity at the end of this phase, ₁ = ₀ + ₁ t₁ = 0 + 4 10 = 40 rad/s In the second phase, the wheel rotates uniformly. Angular velocity, ₁ = 40 rad/s Time, t₂ = 10 s Angle rotated, ₂ = ₁ t₂ = 40 10 = 400 rad In the third phase,