Forces as Vectors: Resolving and Resultants
Draw every force acting on a body as an arrow, add them as vectors to get the resultant, and split any force into components along two perpendicular directions of your choosing.
What a learner can do afterwards
- Resolve a 20 N force at 30° to the horizontal into two components
- Find the magnitude and direction of the resultant of two perpendicular forces
- Draw a diagram showing every force on a body and nothing that is not a force
1 · Read
A tilted force is two forces in disguise: one across and one up, at right angles to each other. With the angle measured from the horizontal, the across part is F times cos and the up part is F times sin. A 30 N force at 30 degrees gives 30 times 0.5, which is 15 N upward, and about 26.0 N across.
Perpendicular forces add through Pythagoras, and the direction comes from tan. A 5 N pull east with a 12 N pull north gives root 169, which is 13 N, pointing about 67 degrees north of east. tan 45 degrees is 1.
A free body diagram shows every force on the body and nothing else. For a book resting on a table, draw gravity down and the normal force up, with each arrow starting on the book. The push of the book on the table acts on the table, so it stays out of the book diagram.
Split tilted forces into parts before you balance anything. Each direction then balances on its own, which turns one tilted problem into two straight line ones.
Split each force into across and up parts, add perpendicular forces with Pythagoras, and draw only forces on the body.
Rewritten readings were written for this dataset.
More to read
Review your force methods
After studying resultant forces, components and free-body diagrams, review how they fit together. Identify any idea you cannot yet explain and return to its teaching material.
Check your force vocabulary
Practise explaining resultant, component, equilibrium and free-body diagram from memory. Accurate use of these terms matters in physics answers. Before attempting practice questions, revisit any definition you cannot explain.
Draw the forces before resolving them
Represent one isolated object in a free-body diagram. Show every external force on that object with a labelled arrow. Do not include forces acting on other objects. Axes and angle labels may help you resolve the forces.
Make the drawing large enough to read. Check the force labels before splitting forces into components.
Link force arrows with motion
Review how vectors connect Newton's laws and net force with motion in one or two dimensions. Draw examples with a pencil, checking that each force arrow agrees with the situation you describe.
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2 · Watch
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Where it sits
Optional connections
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.