# Equilibrium Question: Arbitrary Axis of Rotation?

1. Apr 1, 2015

### cj

Ok, I solved the question posed in the attached image. I did so by using the car's center of mass as the location of my axis of rotation, generated torque and force equilibrium equations, and solved for all unknowns.

When I try to use another location for my axis of rotation, e.g., the point where the front wheels make contact with the ground (thus eliminating the friction forces since their torque arm=0), I get an answer straight away -- but it's not correct!

My experience -- plus my textbooks (Halliday & Serway) -- say selecting any arbitrary location for my axis of rotation is valid (whether you have enough equations to cover the unknowns is a different matter).

QUESTION:
It seems, in this case, the choice is not arbitrary: I must use the COM as the axis of rotation location. WHY? Does it have something to do with the car not being in x-dimension equilibrium?

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2. Apr 1, 2015

### Staff: Mentor

Yes. Try it by putting in the pseudo force -ma at the center of mass. You will find that this gives the right answer. Basically, what you are doing is moving the ma to the same side of the equation as the applied forces (as just another applied force necessary to hold the body in static equilibrium), and then taking moments of those forces about an arbitrary center of rotation. For a body in static equilibrium, it doesn't matter what point you use to take the moments.

Chet

3. Apr 2, 2015

### cj

Ah, THANK YOU - very helpful. I've never dug into fictitious forces - much less utilized them in problem solving. Seems like I need to start. Again, thank you.