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.

A solid body rotates about a stationary axis so that the rotation angl

1.	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.
Answer» `theta=6t-2t^(3)` `omega=(dtheta)/(dt)` `=6-6t^(2)` `alphal=(domega)/(dt)=-12t` `omega=0` at `t=1` sec `(omega)_(0-1)=((int_(0)^(1)omegadt)/(1))=int_(0)^(1)(6-6t^(2))dt` `(alpha)_(0-1)=((int_(0)^(1))alphadt)/(1)=int_(0)^(1)(-12t)` `=-6rad//s^(2)`

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