Final answer:
Without additional information, we cannot determine the time it took to complete the first revolution. However, the angular acceleration can be found using α = (ω - ω0)/t where ω is 32 rad/s and ω0 is the initial angular velocity (zero, starting from rest) over 0.40 s. Then, the number of revolutions can be calculated based on the angular displacement over time.
Step-by-step explanation:
To answer the question about the time it took to make the first complete revolution, we would need additional information such as the constant angular acceleration or the time it took to go from rest to the given angular speed. However, based on the information given in the references, we cannot directly calculate the time for the first revolution without an understanding of the angular acceleration, which was mentioned to be from rest to 32 rad/s in 0.40 s.
Knowing the angular acceleration, the time for the first complete revolution can be calculated using the formula θ = ω0t + (1/2)αt2, where θ = 2π radians (for one revolution), ω0 is the initial angular velocity (zero if starting from rest), α is the angular acceleration, and t is the time. Since there is constant angular acceleration, the first revolution would have taken longer than the second one because the disk started from rest.
For (a) computing angular acceleration and (b) finding the number of revolutions, we can use the following equations:
α = (ω - ω0)/t, and
θ = 0.5*(ω + ω0)*t, respectively, where θ is in radians, and 1 revolution is equal to 2π radians.