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description: show all you work, including units, on separate paper. follow the \problem solving method\. this final exam is cumulative and covers material from the entire course.
instructions: from the list of choices, select the one best answer.
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question 43 of 62
1.6 points
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the angular speed of a flywheel increases from 40 rad/s to 125 rad/s in a time of 4.00 s. what is the angular acceleration of the flywheel?
21.3 rad/s²
41.3 rad/s²
8.25 rad/s²
82.5 rad/s²

Explanation:

Step1: Recall angular acceleration formula

Angular acceleration \(\alpha\) is given by the change in angular velocity \(\Delta \omega\) over time \(\Delta t\), so \(\alpha=\frac{\Delta \omega}{\Delta t}=\frac{\omega_f - \omega_i}{t}\).

Step2: Identify given values

Initial angular velocity \(\omega_i = 40\space rad/s\), final angular velocity \(\omega_f = 125\space rad/s\), time \(t = 4.00\space s\).

Step3: Calculate \(\Delta \omega\)

\(\Delta \omega=\omega_f - \omega_i = 125 - 40 = 85\space rad/s\).

Step4: Calculate angular acceleration

\(\alpha=\frac{85}{4.00}=21.25\approx21.3\space rad/s^2\).

Answer:

21.3 rad/s²