Angular velocity is given by:

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

Average angular acceleration is expresed as:

$\overline{)\begin{array}{rcl}{{\mathbf{\alpha}}}_{{\mathbf{avg}}}& {\mathbf{=}}& \frac{\mathbf{\u2206}\mathbf{\omega}}{\mathbf{\u2206}\mathbf{t}}\end{array}}$

Instantaneous angular acceleration:

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

**(a)**

Angular velocity is:

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

The angular position of a point on the rim of a rotating wheel is given by θ = 4.0 *t* — 3.0*t*^{2} + *t*^{3}, 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?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Rotational Velocity & Acceleration concept. You can view video lessons to learn Rotational Velocity & Acceleration. Or if you need more Rotational Velocity & Acceleration practice, you can also practice Rotational Velocity & Acceleration practice problems.

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Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.