This a rotational kinematics problem since we have an acceleration. We'll need the rotational kinematics equations.

Rotational kinematic equations:

$\overline{){{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{(}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{)}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}_{{\mathbf{f}}}^{{\mathbf{2}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\u2206}}{\mathbf{\theta}}}$

**(a)** the angular velocity changes from -6.00 rad/s to +4.00 rad/s. This means that the angular acceleration should be positive because the angular velocity is becoming more positive.

A wheel is rotating about an axis that is in the z-direction. The angular velocity _{z} is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at = 12.0 s . We have taken counterclockwise rotation to be positive.

(a) Is the angular acceleration during this time interval positive or negative?

(b) How long is the time interval during which the speed of the wheel is increasing?

(c) How long is the time interval during which the speed of the wheel is decreasing?

(d) What is the angular displacement of the wheel from t = 0 s to = 12.0 s ?

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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 Equations of Rotational Motion concept. You can view video lessons to learn Equations of Rotational Motion. Or if you need more Equations of Rotational Motion practice, you can also practice Equations of Rotational Motion practice problems.