5.1 Forces, moments, and equilibrium

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5.1.1 Forces

• A force is a push or a pull
• A force causes acceleration of a mass \[\begin{split} F =& \; m a \; ( =m \ddot{x} = m \dot{v})\\ \end{split}\]
  • acceleration – \(a\)
    • \(a\) is also called \(\ddot{x}\) or \(\dot{v}\)
    • position – \(x\)
    • velocity – \(v\)
    • \(\dot{()}\) the rate of change of \(()\)
• Example
  • Weight – the pull of the earth’s gravity on a body

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Note Mass (\(m\)) can be considered the bodies resistance to a change in its motion (ie inertia))

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5.1.2 Moments

• Similar to a force, a moment is a
  pair of forces that cause twisting \[M = I \alpha\]
  • the angular acceleration – \(\alpha\)
    • \(\alpha\) is also called \(\ddot{\theta}\)
    • \(\dot{\theta}\) – the angular velocity
    • \(\theta\) – the angle (ie the current orientation)
  • \(I\) is the rotational inertia

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Notes

• Moments are also called bending moments or torques
  depending on the application.

• Moments and forces are both described as “generalized forces”

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5.1.3 Equilibrium

• We have already used another important concept, equilibrium

• Forces and changes in momentum remain in balance \[\begin{split} \displaystyle\sum F =& \; m a \\ \displaystyle\sum M =& \; I \alpha \\ \end{split}\]

• Much of biomechanics boils down to applying these equations

• Static equilibrium – the balance of forces that occurs
  when there is no acceleration \[\begin{split} \sum F =& \; 0 \\ \sum M =& \; 0 \\ \end{split}\]