A Ferris wheel starts at rest and builds up to a final angular speed of 0.60 rad/s while rotating through an angular displacement of 2.5 rad.What is its average angular acceleration? A) 0.09 rad/s² B) 11.11 rad/s² C) 0.15 rad/s² D) 0.18 rad/s² E) 0.09 rad/s²

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The average angular acceleration is given by:$$\alpha=\frac{\omega_f-\omega_i}{\Delta t}$$where:* $\omega_f$ is the final angular speed* $\omega_i$ is the initial angular speed* $\Delta t$ is the time intervalIn this problem, the initial angular speed is 0 rad/s, the final angular speed is 0.60 rad/s, and the angular displacement is 2.5 rad. We can use the following equation to find the time interval:$$\Delta t=\frac{\Delta \theta}{\omega_{avg}}$$where:* $\Delta \theta$ is the angular displacement* $\omega_{avg}$ is the average angular speedThe average angular speed is given by:$$\omega_{avg}=\frac{\omega_f+\omega_i}{2}$$Substituting these equations into the first equation, we get:$$\alpha=\frac{\omega_f-\omega_i}{\frac{\Delta \theta}{\omega_{avg}}}=\frac{\omega_f-\omega_i}{\frac{\Delta \theta}{\frac{\omega_f+\omega_i}{2}}}=\frac{2(\omega_f-\omega_i)}{\Delta \theta}$$Substituting the given values, we get:$$\alpha=\frac{2(0.60\text{ rad/s}-0\text{ rad/s})}{2.5\text{ rad}}=\boxed{0.09\text{ rad/s}^2}$$

A Ferris Wheel Starts at Rest and Builds Up to a Final