[{"data":1,"prerenderedAt":21},["ShallowReactive",2],{"formula-en-resultant-magnitude-from-components":3},{"formula":4,"related_topics":13,"alternates":18},{"id":5,"code":6,"slug":7,"title":8,"formula":9,"locale":10,"seo_title":11,"seo_description":11,"content_html":12},143,"statics-resultant-two-components","resultant-magnitude-from-components","Magnitude of a Resultant from Two Components","R = √(Rₓ² + Rᵧ²)","en",null,"\u003Cp>For a planar force system, after algebraically summing the components $R_x=\\sum F_{ix}$ and $R_y=\\sum F_{iy}$, the magnitude of the resultant vector is obtained from the Pythagorean relation:\u003C\u002Fp>\u003Cp>$$R=\\sqrt{R_x^2+R_y^2}$$\u003C\u002Fp>\u003Cp>This formula gives the magnitude of the vector sum of the forces. For a general force system, its moment effect must also be considered separately.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>",[14],{"id":15,"name":16,"path":17},184,"Addition of Forces. Resultant of a Force System","theoretical-mechanics\u002Fstatics\u002Ffundamentals-of-forces-and-moments\u002Faddition-forces-resultant-force-system",{"en":19,"uk":20},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fresultant-magnitude-from-components","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fmodul-rivnodiinoi-za-proektsiiamy",1787712543893]