Rotational kinematic equations:

$\overline{){\mathbf{\omega}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\theta}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{{\mathbf{\omega}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\theta}}}$

For the first round:

- t
_{1}= t s - θ
_{1}= 2π - ω
_{0}= 0 rad/s - α
_{1}= α (constant) - ω
_{1}= ?

For the second round:

- t
_{2}= (t + 0.0865) s - θ
_{2}= 4π rad - ω
_{0}= 0 rad/s - α
_{2}= α (constant) - ω
_{2}= ?

**(a)**

We need an expression that does not have ω (ω_{1}, ω_{2}):

θ_{1} = ω_{0}t_{1} + (1/2)αt_{1}^{2}

2π = 0 + (1/2)(α)(t^{2}) Equation 1

θ_{2} = ω_{0}t_{2} + (1/2)αt_{2}^{2}

A computer disk drive is turned on starting from rest and has a constant angular acceleration. If it took 0.0865 s for the drive to make its second revolution,

(a) how long did it take to make the first complete revolution, and

(b) what is its angular acceleration, in rad/s^{2}?

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