An object rotates with a constant angular acceleration of 10 rad/s², an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its total time of rotation is A) 1.0 s. B) 2.0 s. C) 3.0 s. D) 4.0 s.

Question

Quizplus · Accepted Answer

The total time of rotation can be found using the formula for angular acceleration, $\alpha = \frac{\Delta \omega}{\Delta t}$, where $\Delta \omega$ is the change in angular velocity and $\Delta t$ is the change in time. Given $\Delta \omega = 30 \, \text{rad/s} - 10 \, \text{rad/s} = 20 \, \text{rad/s}$ and $\alpha = 10 \, \text{rad/s}^2$, solving for $\Delta t$ gives $\Delta t = \frac{\Delta \omega}{\alpha} = \frac{20 \, \text{rad/s}}{10 \, \text{rad/s}^2} = 2.0 \, \text{s}$.

An Object Rotates with a Constant Angular Acceleration of 10