When force and displacement are not parallel: the dot product

If a constant force F pushes an object in the same direction as the object moves, for a distance d, then the work done by the force on the object is simple:

• Example: a constant force in direction of motion

But real life is rarely so simple. You need to know how to deal with more complicated situations. For example, what if the force is not in same direction as the motion?

The solution is to find the component of the force which acts along the direction of motion.

• guide to finding the component of force along direction of motion
• Example: Constant force NOT in direction of motion

  The need for "the-component-of-force-in-the-same-direction-as-motion" occurs so frequently that physicists have a special shorthand notation to describe it: the dot product.

• a brief description of the dot product
• a problem in which the dot products helps a LOT

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.