A wheel's uniform angular acceleration is constant. Initially its angular velocity is zero. During the first 1.0 s time interval, it rotates through an angle of 90.0°.

(a) Through what angle does it rotate during the next 1.0 s time interval?

(b) Through what angle during the third 1.0 s time interval?

I know similar questions have been posted before, but none are very helpful to me, so if one could give me a setup of how to do these please! I thought that for a it would be 180 degrees and for b) 270 degree, but its wrong.

To solve this problem, we need to use the equations of rotational motion.

Let's start by defining the given information:
Initial angular velocity, ω₀ = 0 rad/s
Time, t = 1.0 s
Angular displacement, θ₁ = 90.0°

(a) To find the angle rotated during the second time interval, we need to determine the final angular velocity, ω₁.

We can use the following equation of rotational motion:
θ = ω₀t + (1/2)αt²

Since we know the initial angular velocity, ω₀ = 0, and the time interval, t = 1.0 s, we can solve for the angular acceleration, α, using the given angular displacement, θ₁ = 90.0° (convert to radians).

θ₁ = (1/2)αt²
90.0° = (1/2)α(1.0 s)²
90.0° = (1/2)α

Now, we need to calculate α:
α = (2θ₁) / t²
α = 2 * (90.0°) / (1.0 s)²
α ≈ 180.0°/s²

Now that we have the angular acceleration, α, we can use it to find the final angular velocity, ω₁, at the end of the first time interval:
ω₁ = ω₀ + αt
ω₁ = 0 + (180.0°/s²)(1.0 s)
ω₁ ≈ 180.0°/s

Next, we can use the final angular velocity, ω₁, to find the angle rotated during the second time interval:
θ₂ = ω₁t + (1/2)αt²
θ₂ = (180.0°/s)(1.0 s) + (1/2)(180.0°/s²)(1.0 s)²
θ₂ ≈ 180.0° + 90.0°
θ₂ ≈ 270.0°

Therefore, the wheel rotates through an angle of approximately 270.0° during the next 1.0 s time interval.

(b) Similarly, to find the angle rotated during the third time interval, we need to determine the final angular velocity at the end of the second time interval, ω₂.

We can use the same equation of rotational motion:
ω₂ = ω₁ + αt

Now, we can substitute the values we know into the equation:
ω₂ = 180.0°/s + (180.0°/s²)(1.0 s)
ω₂ ≈ 360.0°/s

Finally, we can find the angle rotated during the third time interval using the final angular velocity, ω₂:
θ₃ = ω₂t + (1/2)αt²
θ₃ = (360.0°/s)(1.0 s) + (1/2)(180.0°/s²)(1.0 s)²
θ₃ ≈ 360.0° + 90.0°
θ₃ ≈ 450.0°

Therefore, the wheel rotates through an angle of approximately 450.0° during the third 1.0 s time interval.