Final answer:
The average angular acceleration of a Ferris wheel that increases its angular velocity from rest to 4.2 rad/s over an angular displacement of 3.5 rad is 2.52 rad/s².
Step-by-step explanation:
The average angular acceleration of a Ferris wheel that starts from rest and builds up to a final angular speed of 4.2 rad/s while rotating through an angular displacement of 3.5 rad can be calculated using the kinematic equation:
α = (ω^2 - ω_0^2) / (2θ),
where α is the angular acceleration, ω is the final angular velocity, ω_0 is the initial angular velocity, and θ is the angular displacement. Since the Ferris wheel starts from rest, ω_0 = 0, and the equation simplifies to:
α = (ω^2) / (2θ).
Plugging in the given values:
α = (4.2 rad/s)^2 / (2 × 3.5 rad) = 2.52 rad/s².
Therefore, the average angular acceleration of the Ferris wheel is 2.52 rad/s².