A Ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration? A)9.3 rad/s² B)0.37 rad/s² C)2.6 rad/s² D)0.39 rad/s²

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Quizplus · Accepted Answer

The average angular acceleration ($\alpha$) can be calculated using the formula $\alpha = \frac{\Delta \omega}{\Delta t}$, where $\Delta \omega$ is the change in angular velocity and $\Delta t$ is the change in time. However, without the time, we use the formula that relates angular acceleration to angular displacement ($\theta$) and final angular velocity ($\omega^2$), which is $\omega^2 = \omega_0^2 + 2\alpha\theta$, where $\omega_0$ is the initial angular velocity (0 rad/s since it starts from rest). Rearranging for $\alpha$ gives $\alpha = \frac{\omega^2 - \omega_0^2}{2\theta}$. Substituting the given values ($\omega = 1.9$ rad/s, $\omega_0 = 0$ rad/s, $\theta = 4.9$ rad) gives $\alpha = \frac{(1.9)^2}{2*4.9} = 0.37$ rad/s$^2$.

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