A wheel is rotating about an axis that is in the Z-direction. The angular veloci

Question

A wheel is rotating about an axis that is in the Z-direction. The angular velocity w_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 16.0 s .We have taken counterclockwise rotation to be positive. How long is the time interval during which the speed of the wheel is increasing? Express your answer with the appropriate units. How long is the time interval during which the speed of the wheel is decreasing? Express your answer with the appropriate units. What is the angular displacement of the wheel from t = 0 s to t = 16.0 s ?

Explanation / Answer

Find the acceleration = (4-(-6.0))/16 = 10/16 rad/s²
(t) = o + (10/16)*t = -6.0 + (10/16)*t >0
The speed is increasing from = 0 to = 4
= 0.625, so speed is increasing for 6.4 seconds

2.) Speed is decreasing for the first 9.6 seconds.

3.) f^2 = i^2 + 2
= (4^2-6^2)/2(0.625)
= (-20/1.25) = -16 radian

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