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 is at , increases linearly with time and is at . We have taken counterclockwise rotation to be positive. Is the angular acceleration during this time interval positive or negative? During what time interval is the speed of the wheel increasing? During what time interval is the speed of the wheel decreasing? What is the angular displacement of the wheel at 7 seconds? Please use all the formulas and show work in step by step processes with detailed information. Thank you.

Explanation / Answer

a)we know that angular acceleration a = (?2-?1)/t t = 7 sec ?1 = -6.00 rad/s ?2 = +8.00m/s Then angular acceleration a = (8 +6)/7 = +2rad/sec2 Thus angular acceleration during this time interval positiveor negative. b) for the wheel to stop that means ?2 = 0 then t = -?1/a = +6/2 = 3 sec Thus upto t = 3 sec speed of the wheel is decreasing and Hencefor next four sec its angular speed increases from 0 rad/sec to 8rad/sec. c) we know that net angular displacement ? =?1*t + (1/2)at2 = -6*7 + (1/2)*2*(7)2 = 7 rad

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