Equations of Rotational Motion Video Lessons

Concept

# Problem: A computer disk drive is turned on starting from rest and has a constant angular acceleration. If it took 0.750 seconds for the drive to make its second revolution,1. How long did it take to make the first complete revolution?2. What is its angular acceleration in rad/s2?

###### FREE Expert Solution

(a)

For the two revolutions, time, t' = t + 0.750 s

The angular displacement for one revolution, Δθ = 2π rad

For two complete revolutions, 2Δθ= 4π rad

The rotational kinematic relation:

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

For the first complete revolution:

$\begin{array}{rcl}\mathbf{2}\mathbf{\pi }& \mathbf{=}& \mathbf{0}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\alpha }{\mathbf{t}}^{\mathbf{2}}\end{array}$

4π = αt2

For two complete revolutions:

$\begin{array}{rcl}\mathbf{4}\mathbf{\pi }& \mathbf{=}& \mathbf{0}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\alpha }{\mathbf{\left(}\mathbf{t}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{750}\mathbf{\right)}}^{\mathbf{2}}\\ \mathbf{8}\mathbf{\pi }& \mathbf{=}& \mathbf{\alpha }\mathbf{\left(}{\mathbf{t}}^{\mathbf{2}}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{t}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{5625}\mathbf{\right)}\end{array}$

8π = α(t2 + 1.5t + 0.5625)

Dividing the expression for two complete revolutions and that of one complete revolution:

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###### Problem Details

A computer disk drive is turned on starting from rest and has a constant angular acceleration. If it took 0.750 seconds for the drive to make its second revolution,

1. How long did it take to make the first complete revolution?

2. What is its angular acceleration in rad/s2?