Equations of Rotational Motion Video Lessons

Concept

# Problem: A wheel rotates with a constant angular acceleration of 3.50 rad/s2. 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

###### FREE Expert Solution

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 t1 = 2.00 s, the angular displacement becomes:

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

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###### Problem Details

A wheel rotates with a constant angular acceleration of 3.50 rad/s2. 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.