# Chapter 8 - Rotational Kinematics - Problems - Page 214: 32

$t=12.5s$

#### Work Step by Step

We know $\alpha=-4rad/s^2$, $\omega=-25rad/s^2$ and $\theta=0$ We know that $$\theta=\omega_0t+\frac{1}{2}\alpha t^2$$ However, we also have $\omega_0=\omega-\alpha t$ Therefore, $$\theta=(\omega-\alpha t)t+\frac{1}{2}\alpha t^2$$ $$\theta=\omega t-\alpha t^2+\frac{1}{2}\alpha t^2$$ $$\theta=\omega t-\frac{1}{2}\alpha t^2$$ We now plug the numbers in: $$-25t+2t^2=0$$ Ignoring $t=0$, we find $t=12.5s$

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