Obtain Eq. (7.38) `omega= omega_0 + alphat` from first principles.

Explanation

The angular acceleration is uniform, hence
`(domega)/(dt)=alpha` = constant (i)
Integrating this equation,
`omega=intalphadt+c`
`=alphat+c` (as `alpha` is constant)
At `t = 0, ω= ω_(0)` (given)
From (i) we get at `t=0,ω=c=omega_(0)`
Thus, `ω = αt + ω_(0)` as required.
With the definition of `ω= d θ //dt` we may integrate Eq. (7.38) to get .This derivation and the derivation of Eq. (7.40) is left as an exercise.