Rev. 1 REVIEW SHEET #9: Rigid-Body Static Equilibrium Definition: An extended body is in equilibrium if the following two conditions are met: First Condition: The (vector) sum of all external forces acting on the body is zero. 0ext cm F Ma = = ∑ r r Hence the acceleration of the body’s Center of Mass is zero. Second Condition: The sum of the torques due to all external forces acting on the body, with respect to any specified point, is zero. 0ext I τ α = ⋅ = ∑ r r Hence the angular acceleration of the object about any axis is zero. In this course we have restricted our discussion to extended rigid bodies that were in static equilibrium , i.e. in addition to meeting the above two conditions these bodies were also at rest with respect to both translation and rotation. Center of Gravity: The gravitational force we usually call weight does not act at a single point of an extended body. Instead, it is distributed over the entire body. However, the torque produced by a body’s weight can be calculated by assuming that
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