# Chapter 8 - Rotational Kinematics - Problems - Page 214: 26

$3.37s$

#### Work Step by Step

1) Find the angular acceleration We have $\omega_0=1.05\times10^4rad/s$, $\omega=3.14\times10^4rad/s$ and $\theta=1.88\times10^4rad$ $$\alpha=\frac{\omega^2-\omega_0^2}{2\theta}=2.33\times10^4rad/s^2$$ 2) In the 2nd situation, we have $\omega_0=0$, $\omega=7.85\times10^4rad/s$ and $\alpha=2.33\times10^4rad/s^2$ The time it takes the bit to reach its maximum speed is $$t=\frac{\omega-\omega_0}{\alpha}=3.37s$$

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