02062009

# 02062009 - Equilibrium for a Particle vs Rigid Body For a...

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Equilibrium for a Particle vs. Rigid Body For a particle, Σ F i = R = 0 is a sufficient condition for equilibrium For a 3-dimensional rigid body, Σ F i = R = 0 is a necessary but insufficient condition for equilibrium because the forces acting on it are usually not concurrent. Non-concurrent forces may produce rotation – a moment Equilibrium for rigid body: Σ F i = R = 0 and Σ M i = M = 0.

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Line of Action and Moment Although F and F” have the same magnitude and direction, they have different effects on the body because the forces have different lines of action. F and F” will produce the same linear motion at the body’s center of mass but different rotational motion.
Moment of a Force Moment is a vector (has magnitude and direction) Magnitude: product of the magnitude of the force and the perpendicular distance from the line of action of force to the axis of rotation M O = Fd, where d is called the moment arm Direction: “+” moment produces CCW rotation

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