MDCAT Physics · Physics · Vectors and equilibrium. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A vector has a size and a direction, so two vectors cannot be added like ordinary numbers. The easy method is to split each vector into two parts at right angles, called rectangular components: one along the x-axis and one along the y-axis.
For a vector A at angle θ to the positive x-axis, the x-component is A cos θ and the y-component is A sin θ. To add several vectors, add all the x-components to get Rx and all the y-components to get Ry.
These two give the resultant. Its size comes from Pythagoras and its direction from tan θ = Ry/Rx. Look at the signs of Rx and Ry to choose the correct quadrant.
Students use cos for the x-component every time. If the angle is measured from the y-axis, the x-component is A sin θ, so always check which axis the angle is measured from.
Answer: 6.9 N along the positive x-axis.
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