1. 2D – Force Systems Choose appropriate coordinate system for situation. Standard x-horizontal and y-vertical system may not be the best choice! Relate forces to the chosen coordinate system using proper component notation. Determine magnitude and direction of a vector from components.

5. Moments Forces that are applied to an object can cause translation or rotation. Forces that result in rotation are called moments (torques). Moments are rotational forces – forces in a direction perpendicular to the plane containing the rotational motion. The order of multiplication is important! r x F ≠ F x r. Using the scalar form of the cross-product only provides magnitude information. The angle, , is the angle measured from r to F in the positive angular direction. You must define the axis you are rotating about in order to properly define r. Maximum moment occurs when r and F are perpendicular. M = rF

6. Vector Product (Cross-product) There are two different methods for determining the vector product between any two vectors: The Determinant method and the Cyclic method Determinant Method Cyclic Method Rewrite the j term as to get an identical expression

7. Varignon’s Theorem – The moment of a force about any point is equal to the sum of the moments of the components of the force about the same point. M o – Moment about point o. R – Resultant Force. P – Non-Cartesian component of R. Q – Non-Cartesian component of R. This is true for any number of components!