Unformatted text preview: asses in the body. Then use the definition of center
of mass to get the result. ”
tgrav = ‚ ri ä mi g = ‚ mi ri ä g = IM rcm M ä g = rcm ä M g
i i Equilibrium
The Conditions for Equilibrium
If a body is in equilibrium then there is no acceleration and there is no angular acceleration. This implies that the net force and the net torque
must vanish. F net = 0 and tnet = 0
For the examples we will consider all possible rotation will be in a plane and thus we only need to consider torques relative to an axis. The Origin (or Axis) is Arbitrary
When considering an equilibrium problem sometimes the choice of axis is clear. Often in isn't clear, though, and there isn't a natural choice.
The key point is that the choice of origin or axis is arbitrary. When something is arbitrary then we have the luxury of making a choice that
simplifies the problem.
The basic result is this: If the torques balance about one origin and the forces balance then the torques balance about any origin. If the vector
from one origin to another is r0 . If ri is the vector from the new origin at r0 to the mass mi and ri is from the first origin to the mass then ” ”£ ”
ri = ri + r0 .
£ £ Take the net torques about these axes to be tnet and tnet . If tnet = 0 and F net = 0 then tnet = 0. ”
0 = tnet = ‚ ri ä F i = ‚ ri ä F i + r0 ä ‚ F i = tnet + 0
i This proves our result. i i...
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