I have a question about Newton's Second Law and Inertial Frames of Refrence. It is canon that Newton's Second Law is only applicable in an inertial frame of refrence. Newton's Second Law is the net force acting on a body is equal to the time rate of change of the body's linear momentum. Expressed mathematically N.S.L is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum[/tex]F= dp/dt = d(mv)/dt = (dm/dt)v+ m(dv/dt)

Lets define a general velocity vector using arbitrary coordinates.The Einstein Summation Convention is being used. Letv= v^{a}e_{a}

then (dv/dt) = (dv^{a}/dt)e+ v_{a}^{a}(de/dt). Substituting this into the equation above and factoring one can arrive at_{a}

[tex]\sum[/tex]F= [(dm/dt)v^{a}+ m(dv^{a}/dt)]e+ mv_{a}^{a}(de/dt)._{a}

In regular cartesian coordinates, the last term in zero. My question is, can one apply N.S.L. in an accelerating frame of refrence by adding the last term, mv^{a}(de/dt), instead of adding ficticious forces?_{a}

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# Newton's Second Law and Inertial Frames Of Refence

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