Question
<p>A disk is initially at rest and undergoes an angular acceleration [α]=2rad/s<sup>2</sup> for 2 seconds.  Abruptly teh angular acceleration becomes [α]=0rad/s<sup>2</sup> and the disk continues to rotate for 3 more seconds.  After these 5 seconds, the disk begins to undergo an angular deceleration of magnitude [α]=4rad/s<sup>2 </sup>until it comes to rest.  How many rotations will the disk have turned during its entire motion.</p>
Explanation / Answer
initial angular acceleration of the disc is 1 =2rad/s^2 time t1 =2s now angular acceleration is = 0rad/s^2 time t2 =3s so angular speed is constant for this time t =5s 2 =1+t but due to initial at rest 1 =0 2 =2*5 =10rad/s if we take 2 is initial speed of the disc before go to deceleration 3^2-2^2 =2 but disk will be come to rest finally 3=0 the deceleration acceleration = -4 rad/s^2 there fore -2^2 =2(-4) angular displacement = (10)^2/8 =12.50 180 degree = rad 10 = /180 rad = 0.017444 rad 12.50 =0.21805 rad but 1 revolution =2 rad 1 rad =1/2 revolutions =0.159235 rev for 0.21805 rad = (0.21805)(0.159235) rev =0.034721 rev 180 degree = rad 10 = /180 rad = 0.017444 rad 12.50 =0.21805 rad but 1 revolution =2 rad 1 rad =1/2 revolutions =0.159235 rev for 0.21805 rad = (0.21805)(0.159235) rev =0.034721 rev