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19: N6) Statics and Springs

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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    • 19.1: Conditions for Static Equilibrium
      A body is in equilibrium when it remains either in uniform motion (both translational and rotational) or at rest. Conditions for equilibrium require that the sum of all external forces acting on the body is zero, and the sum of all external torques from external forces is zero. The free-body diagram for a body is a useful tool that allows us to count correctly all contributions from all external forces and torques acting on the body.
    • 19.2: Springs
    • 19.3: Examples
      In applications of equilibrium conditions for rigid bodies, identify all forces that act on a rigid body and note their lever arms in rotation about a chosen rotation axis. Net external forces and torques can be clearly identified from a correctly constructed free-body diagram. In setting up equilibrium conditions, we are free to adopt any inertial frame of reference and any position of the pivot point. We reach the same answer no matter what choices we make.

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