What is component method?

Question

what is the definition of component method in physics.?

Answer 1

It's a method of vector summing where you take the x- components of each of the vectors and add them together to get the x-components of the total. Do the same for the y-components.

Use those values and the Pythagorean Theorem and trig to get the direction and magnitude of the total vector.

Answer 2

Question: how do you add or subtract vectors? Answer: Use the component method.

A vector is a line segment with a magnitude (length) and a direction (slope). Adding two directions and magnitudes can be done graphically, but not directly using math.

The component method is the concept that you can resolve vectors into two independent (therefore perpendicular) vectors (say, in the x and y directions). And, you can "put a vector back together" simply, using the distance formula and the slope of the line.

So, the component form and the direction/magnitude forms are just two different ways of specifying a vector.

The math to convert back and forth between them is the same as for three identical things that you were introduced to as being separate:  the Pythagorean theorem, the equation of a circle, and the distance formula.

Let's do an example: Assume you go √3 miles due East, and 1 mile due North, how far have you gone? From A² = B² + C²,

A = √B² + C² = 2

Or, same using the distance formula, Dist = √X² + Y² = 2. Or, use X² + Y² = R², which is the equation of a circle. All the same, right?

Now, if you want the angle, how do you get it? From the slope of a line, angle = arctan [(y2-y1)/(x2-x1)].

Using a triangle, arctan (opp/adj) = arctan (Y/X), using the unit circle, X=R*cos Θ , Y = R*sin Θ and tan Θ = Y/X. Again, all the same!

So, to add two vectors, resolve them into components in the X and Y directions, add the components together, then convert back.