Rotational Velocity & Acceleration Video Lessons

Concept

# Problem: The angular position of a point on the rim of a rotating wheel is given by θ = 4.0  t — 3.0t2 + t3, where θ is in radians and t is in seconds. What are the angular velocities at:(a) t = 2.0 s and (b) t = 4.0 s? c) What is the average angular acceleration for the time interval that begins at  t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at: (d) the beginning and (e) the end of this time interval?

###### FREE Expert Solution

Angular velocity is given by:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\frac{\mathbf{d}\mathbf{\theta }}{\mathbf{d}\mathbf{t}}}$

Average angular acceleration is expresed as:

$\overline{)\begin{array}{rcl}{{\mathbf{\alpha }}}_{{\mathbf{avg}}}& {\mathbf{=}}& \frac{\mathbf{∆}\mathbf{\omega }}{\mathbf{∆}\mathbf{t}}\end{array}}$

Instantaneous angular acceleration:

$\overline{){\mathbf{\alpha }}{\mathbf{=}}\frac{\mathbf{d}\mathbf{\omega }}{\mathbf{d}\mathbf{t}}}$

(a)

Angular velocity is:

$\begin{array}{rcl}\mathbf{\omega }& \mathbf{=}& \frac{\mathbf{d}\mathbf{\left(}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{t}\mathbf{-}\mathbf{3}\mathbf{.}\mathbf{0}{\mathbf{t}}^{\mathbf{2}}\mathbf{+}{\mathbf{t}}^{\mathbf{3}}\mathbf{\right)}}{\mathbf{d}\mathbf{t}}\\ & \mathbf{=}& \mathbf{4}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{t}\mathbf{+}\mathbf{3}{\mathbf{t}}^{\mathbf{2}}\end{array}$

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###### Problem Details

The angular position of a point on the rim of a rotating wheel is given by θ = 4.0  t — 3.0t2 + t3, where θ is in radians and t is in seconds. What are the angular velocities at:

(a) t = 2.0 s and

(b) t = 4.0 s?

c) What is the average angular acceleration for the time interval that begins at  t = 2.0 s and ends at t = 4.0 s?

What are the instantaneous angular accelerations at:

(d) the beginning and

(e) the end of this time interval?