A solid body rotates about a stationary axis so that the rotation angle `theta` varies with time as `theta=6t-2t^(3)` radian. Find
(a) the angular acceleration at the moment when the body stops and
(b) the average value of angular velocity and angular acceleration averaged over the time interval between `t=0` and the complete stop.

Explanation

`theta=6t-2t^(3)`
`omega=(d theta)/(dt)=6-6t^(2)`
`alpha=(domega)/(dt)=-12t`
(a) When the body stops,`omega=0=6-6t^(2)impliest=1 s`
`alpha=-12t=-12 rad//s^(2)`
`t=0, theta_(1)=0`
`t=1. theta_(2)=6-2(1)^(3)=4`
(b) `undersetomega(-)=(theta_(2)-theta_(1))/(t_(2)-t_(1))`
`=(4-0)/(1-0)=4 rad//s`
`t=0, omega_(1)=6`
`t=1 s, omega_(2)=0`
`undersetalpha(-)=(omega_(2)-omega_(1))/(t_(2)-t_(1))`
`(6-0)/(1-0)=6 rad//s^(2)`