An object, starting from rest at the origin, rotates with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$is in radians/s², t is in seconds, c = -3.0 rad/s², and d = 0.40 rad/s⁴. At time t = 2.0 s, the rotation (in radians) the object has made is A) -1.1 rad. B) 1.1 rad. C) -4.9 rad. D) -5.5 rad.

Question

Quizplus · Accepted Answer

The angular displacement $\theta$ can be found by integrating the angular velocity, which is the integral of angular acceleration $\alpha$. First, integrate $\alpha = c + dt^2$ to find angular velocity $\omega$, then integrate $\omega$ to find $\theta$. After performing these integrations and evaluating at $t = 2.0$ s, the result is $-4.9$ rad.

An Object, Starting from Rest at the Origin, Rotates with an Angular