This a rotational kinematics problem due to the fact that we have actually an acceleration. We"ll need the rotational kinematics equations.

You are watching: A wheel is rotating about an axis that is in the z-direction

Rotational kinematic equations:

ωf=ω0 + αt∆θ=12(ω0+ωf)t∆θ=ω0t +12αt2ωf2=ω02+2α∆θ

(a) the angular velocity changes from -6.00 rad/s to +4.00 rad/s. This means that the angular acceleration should be positive since the angular velocity is becoming an ext positive. A wheel is rotating about an axis the is in the z-direction. The angular velocity z is -6.00 rad/s at t = 0, increases linearly through time, and is +4.00 rad/s in ~ exttiptt = 12.0 s . We have taken counterclockwise rotation to it is in positive.

(a) Is the angular acceleration throughout this time interval confident or negative?

(b) how long is the moment interval throughout which the speed of the wheel is increasing?

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

(d) What is the angular displacement that the wheel indigenous t = 0 s to exttiptt = 12.0 s ?

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