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rajan jha Grade:
        

A solid body rotates about a stationary axis according to the law theta=at-bt^3,where a=6 rad/s and b=2 rad/s^3.Find the mean values of the angular velocity and acceleration over the interval between t=0 and the time,when the body comes to rest.

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

@ = at - bt3               ...............1


d@/dt = W = a-3bt2             ...............2


dW/dt = alfa = -6bt           ............3


body comes to rest when angular velocity  becomes 0


a - 3bt2 = 0


    t = (a/3b)1/2 


mean value of angular velocity = (@t - @0)/t


   @0=0


  @t= a(a/3b)1/2 - b(a/3b)3/2


      = a(a/3b)1/2[1-1/3]


      =(2a/3)(a/3b)1/2


mean value of angular velocity = 2a/3(a/3b)1/2/t = 2a/3 = 4rad/sec


 


now mean value of angular accleration = change in angular velocity/t = (Wt-W0)/t


at t=0  W=a , at T=t  Wt = 0


mean value = a/t = (3ab)1/2 


                 =(36)1/2=6rad/sec2


 

6 years ago
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