A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t³, where θ is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s? A) −1.0 rad/s² B) −24 rad/s² C) −2.0 rad/s² D) −4.0 rad/s² E) −3.5 rad/s²

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Quizplus · Accepted Answer

The angular acceleration is found by taking the second derivative of the angular position equation with respect to time. The given equation is θ = 3.0 − 2.0t^3. The first derivative (angular velocity) is dθ/dt = -6.0t^2, and the second derivative (angular acceleration) is d²θ/dt² = -12t. Substituting t = 2.0 s into the second derivative gives an angular acceleration of -24 rad/s².

A Wheel Rotating About a Fixed Axis Has an Angular