The Physics Philes, lesson 64: Equilibrium in Two Easy Steps!

For the past…it seems like forever…we’ve been talking objects that accelerate and we’ve devoted months to figuring out how it all works. But, in the real world, we don’t always want things to accelerate. You know, like buildings and couches and benches or bridges. Those types of things aren’t very useful if they fall over.

So this week we’ll start a discussion on equilibrium and elasticity. We’ll start off by talking about what it take for an object to be in equilibrium.

Equilibrium, as we learned a very, very long time ago, just means that a body isn’t accelerating in an inertial frame of reference. For a particle (or a body we can model as a particle, this is pretty easy. The body is in equilibrium whenever the vector sum of the forces acting on the body is zero. However, that isn’t really representative of real-world situations. In order for an extended body to be in equilibrium, two conditions need to be met.

1. For an extended body to be in equilibrium, the center of mass must have zero acceleration. There will be zero acceleration if the vector sum of all external forces acting on the body is zero. This can, of course, be expressed in math form. If that makes things easier for you.

Screen shot 2013-09-08 at 12.22.34 PM

Which means that:

Screen shot 2013-09-08 at 12.25.01 PM

Screen shot 2013-09-08 at 12.25.17 PM

Screen shot 2013-09-08 at 12.25.34 PM

2. This is necessary, but not sufficient, for an extended body to be in equilibrium. The second condition is for the body in question to have no tendency to rotate. This is based on the dynamics of rotational motion that we’ve been discussing over the past several weeks. A rigid body in an inertial frame of reference is not rotating about a certain point has an angular momentum of zero about that point. For the body to not rotate about that point, the rate of change of angular momentum must also be zero. That means that the sum of torques from all the external forces must be zero, as well. This has to be true at any point in a rigid body if that rigid body has any chance to be in equilibrium. That brings us to the second condition for equilibrium:

Screen shot 2013-09-08 at 12.43.41 PM

In other words, the sum or the torques due to all external forces acting on the body, with respect to any specified point, must be zero.

These conditions for equilibrium applies when the body is at rest (called static equilibrium), as well as when the body is moving without rotation.

OK! Thus ends the introduction to equilibrium. We’ll continue the discussion next week with a little center of gravity action.

Featured image credit: Kevin Cole

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Mindy is an attorney and Managing Editor of Teen Skepchick. She hates the law and loves stars. You can follow her on Twitter and on Google+.

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