A wheel is rotating about an axis that is in the zdirection

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 = 18.0 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=0s to t=18.0s?

Solution

A) angular acceleration = [4 - (-6)]/18 = 0.555 /s^2

Hence positive

B) time for which speed is increasing = [4-0]/0.555 = 7.272 sec

C) time for which speed is decreasing = [0- -6]/0.555 = 10.8108 sec

d) s = ut + 0.5at^2

= -6*18 +0.5*0.625*18*18 = -6.75 rad