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yes , u can apply newtons 2nd law in a non-inertial frame but u hav to consider the pseudo force and modify the equation accordingly
for example ,
we can take a non inertial frame which has only transational acceleration say 'α'...
then 2nd law equation get modified to
m*dv/dt = F - mα
thus u can see here there is only a simple modification u hav to consider.....
Yes,newton's second law can be applied in non-inertial frame of reference by taking proper pseudo forces in consideration.
Non-inertial frame is accelerated frame,so you take system having pseudo acceleration opposite to the acceleration of the frame & equal in magnitude.
It could be equivalently stated that you make the non-inertial frame an inertial one the moment you take opposite acceleration working on the system(pseudo accn & force)
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