What Is the Component Method of Physics?

The component method is a means of adding different vectors to one another in physics. It enables the addition of right-angled vector components to find a resultant vector having a magnitude and direction that depends on the individual components added.

The component method is commonly used in Cartesian coordinate systems, where the vector components of the individual vectors being added are perpendicular to one another. The method can also be used in other coordinate systems, such as curvilinear and polar systems. First-time users of the coordinate method are recommended to draw arrows with heads and tails that graphically represent the magnitude and direction of the components being added. This visualization solidifies the method, making direct application easier later on.

A firm grasp of the Pythagorean Theorem is a perquisite to applying the component method in Cartesian space, as the resultant vector from adding the perpendicular components is found as the hypotenuse of the right triangle that results when the orthogonal components are added with a straight line connecting the tips of the arrows. Special attention should be paid to the choice of positive and negative directions; the most common convention is to use right and up to represent positive and down and left to represent negative.