A wheel is rotating about an axis that is in the z -direction. The angular veloc

Question

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 t = 16.0 s . We have taken counterclockwise rotation to be positive.

Part A

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

Part B

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

Express your answer with the appropriate units.

Part C

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

Express your answer with the appropriate units.

Part D

What is the angular displacement of the wheel from t = 0 s to t = 16.0 s ?

Explanation / Answer

A) angular acceleration = [4 - (-6)]/16 = 0.625 /s^2

Hence positive

B) time for which speed is increasing = [4-0]/0.625 = 6.4s

C) time for which speed is decreasing = [0- -6]/0.625 = 9.6s

d) s = ut + 0.5at^2

= -6*16 +0.5*0.625*16*16 = -16 rad

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