# Can we change frame of reference twice in a single problem?

My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and inclined plane parallel to the table, somewhat opposite to the block. Can the two equations I make be from the Free Body Diagram (FBD) of incline, in GROUND frame, and FBD of block in the INCLINED-PLANE frame? Or do I need to solve in a single frame(either GROUND or INCLINED-PLANE)?

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## 1 Answer

I'd recommend that you stick to one frame, otherwise you'll have to make coordinate transformations to make your equations consistent and that's significantly more work than it's worth.

Also, be careful that if the inclined plane accelerates (which it will if I understand your setup correctly) then you have to introduce so-called fictitious forces to solve the problem correctly in the incline's (non-intertial) frame, and that's also, in this case, probably more trouble than it's worth in my opinion.

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which frame should I choose, then? In the ground frame, the block's motion seems complicated and in the inclined-plane frame, the inclined-plane's motion seems complicated. Further I find myself unable to imagine in the incline frame. –  Ashish Gaurav Mar 21 '13 at 9:25
I'd recommend that you use the ground frame. Having done this problem before, I can tell you that's it's not that bad; you just have to be careful not to miss any forces when you draw your FBDs. Pay special attention to contact forces between the block and the inclined plane. –  joshphysics Mar 21 '13 at 9:27
thank you so much –  Ashish Gaurav Mar 21 '13 at 9:28