Why do we need Newton's First law? And how the First law works?

This must have been asked before. But never mind here I ask it again to convince myself.



Newton's Second law says [itex]\vec{F}[/itex] = m[itex]\vec{a}[/itex]

Now if we put [itex]\vec{F}[/itex] = 0 here we get [itex]\vec{a}[/itex] = 0 which is Newton's First law.

So why do we need to state First law as a separate law?



Before I asked this I did little bit of searching. And what I got is - First law is necessary to define the Inertial reference frame on which Second law can be applied.



But why can't we just use Newton's second law to define Inertial frame? We can say [itex]\vec{F}[/itex] = m[itex]\vec{a}[/itex] is the Second law. So if [itex]\vec{F}[/itex] = 0 but [itex]\vec{a}[/itex] [itex]\neq[/itex] 0 (or vice versa) then the frame is non inertial.



One can say (can one?), we cannot apply Second law to define Inertial reference frame because the Second law in valid only in Inertial frame. Thus unless we know in advance that a frame is Inertial, we cannot apply the Second law.

But then why this is not a problem for first law? Why don't we need to know in advance if a frame is inertial to apply first law.



As an end note: I am an intro physics student. So please point out to me if I am missing any obvious thing.

Thanks a lot, in advance, for your help!



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