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Obtain Eq. (7.38) from first principles. |
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Answer» Solution :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. |
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