For a rigid body at rest, there is no pivot point since there is no rotational motion. For the purposes of calculating torques, any point within the body can be used as a mathematical pivot point.
For the types of problems we will be doing, there will be two unknown forces acting at different points within the rigid body. Our example: the pulling force exerted upward by the bicep muscle, and the pushing force exerted downward by the humerus bone at the elbow on the human forearm while it is held horizontal supporting a weight in the hand.
While the elbow serves as an obvious pivot point for the arm, the reason we choose it as a pivot point for calculating torques is that by this choice, one of the unknown forces is eliminated from the torque equilibrium equation.
The general procedure for solving for the two unknown forces is this:
In problems involving human limbs and joints, the two forces (muscle force and joint contact force) are large (typically hundreds of Newtons), are generally opposite in direction (NOT antiparallel, though), and the bigger of the two forces points upward because it must oppose both the other force and the weight.
Common pitfalls include: inability to visualize or calculate lever-arm lengths, inability to use supplementary and complementary angles to set up calculation of force components, assuming incorrectly that the given angles are to be used in torque or force component equations.
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