A point on the rim of a disc starts circular motion from rest and after time t, it gains an angular acceleration given by `alpha=3t-t^(2)`. Calculate the angular velocity after 2 s.

Explanation

Angular acceleration, `alpha=(domega)/(dt)=2t-t^(2)`
`rArr" "int_(0)^(omega)domega=int_(0)^(t)(3t-t^(2))dtrArromega=(3t^(2))/(2)-(t^(3))/(3)`
At `2s," "omega=(10)/(3)"rad s"^(-1)`