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`        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

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

```
6 years ago
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