Question

A solid body rotates about a stationary axis according to the law, what is the mean value of angular velocity

Answer 1

@ = at - bt3               ...............1d@/dt = W = a-3bt2             ...............2dW/dt = alfa = -6bt           ............3body comes to rest when angular velocity  becomes 0a - 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)1/2mean 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)/tat t=0  W=a , at T=t  Wt = 0mean value = a/t = (3ab)1/2                  =(36)1/2=6rad/sec2