FROM MY PT SCHOOL NOTES · FUNCTIONAL ANATOMY & BIOMECHANICS · CHAPTER 7
How Do You Combine Forces Before Calculating a Resultant?
Before calculating torque or planning a mechanics explanation, the course asks students to identify vector magnitude, direction and reference axes.
Describe the vector accurately
A scalar has magnitude; a vector has magnitude and direction. In the original biomechanics course, forces are vectors, and their direction matters for the resulting movement or load.
Draw the chosen reference frame and state whether angles are measured from the horizontal, vertical or lever. Many wrong answers begin with an unstated angle.
Separate perpendicular components
In a simple two-dimensional system, a vector can be divided into horizontal and vertical components using trigonometry. For a 100 N force at 30° above the horizontal, the horizontal component is approximately 86.6 N and the vertical component 50 N.
These are newly written teaching values. They assume the angle is defined from the positive horizontal axis; changing that convention changes the signs or formulas.
Combine and interpret the resultant
Parallel and perpendicular forces may be added as vectors using component sums. For example, independent 30 N east and 40 N north forces produce a resultant magnitude of 50 N to the northeast, with a direction set by the component ratio.
A resultant describes the combined external forces in the chosen model. It does not automatically reveal the internal load on a real joint or the clinical significance of that load.
Quick check: What is the magnitude of the resultant of 30 N east and 40 N north?
50 N, using the Pythagorean theorem because the two component vectors are perpendicular. The direction also matters and must be specified separately.
Try the mechanics on a real task
Example: A 100 N force points up and to the right with components of 60 N horizontally and 80 N vertically.
Work through the reasoning
Answer: Its magnitude is √(60² + 80²) = 100 N, with direction determined by the two components. These are the same force expressed in components—not three independent forces to be added together.
Common trap: Adding the original force to its components and double-counting it. Remember: Resolve a vector into parts or recombine parts into a resultant, but not both.
Sources: my original FABIO lectures: FABIO Principles.pdf; FABio Sample Calculation Problems.pdf. Explanatory examples are newly written. This is a conceptual mechanics lesson, not a treatment instruction. Publisher or lecture figures are not reproduced.
