Resultant Force

Trigonometry · Axiom Academy

EXAMPLE Resultant Force Using Components Learn to find the magnitude and direction of a resultant force by breaking vectors into components. Excellent work! You've successfully found the resultant force using component method. Here's what we learned: Component Method: Breaking vectors into x and y components using cosine (for x) and sine (for y) makes complex problems manageable. Angles Matter: Always measure angles from the positive x-axis (standard position). Force at 120° has a negative x-component and positive y-component. Sum Components Separately: Add all x-components together, then all y-components together, before finding the resultant. Pythagorean Theorem: Use |R| = √(Rₓ² + Rᵧ²) to find the magnitude of the resultant from its components. Direction from Arctangent: θ = tan⁻¹(Rᵧ/Rₓ) gives the angle. Pay attention to which quadrant your resultant is in! This component method is essential for solving any vector addition problem in physics and engineering. You can apply this same technique to velocity, acceleration, displacement, and more!

This is the written version of the interactive lesson above. See the full Trigonometry course.