Angular displacement is expressed as:

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

**(a)**

At t_{1} = 2.00 s, the angular displacement becomes:

$\begin{array}{rcl}{\mathbf{\theta}}_{\mathbf{1}}& \mathbf{=}& \mathbf{(}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{)}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{50}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{.}{\mathbf{00}}^{\mathbf{2}}\mathbf{)}\end{array}$

A wheel rotates with a constant angular acceleration of 3.50 rad/s^{2}. If the angular speed of the wheel is 2.00 rad/s at t = 0

(a) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.30 s.

rad

(b) Find the angular speed when t = 3.30 s.

rad/s

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