OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) resolving a vector into two perpendicular components; F x = F cos i ;…
Full specification wording
Scalars and vectors: (d) resolving a vector into two perpendicular components; F x = F cos i ; F y = F sin i .
Resolving splits one vector into two perpendicular components that together have the same effect.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 4
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Resolving splits one vector into two perpendicular components that together have the same effect. Draw the vector F as the hypotenuse of a right-angled triangle, with the two components along chosen perpendicular axes. If the angle i is measured from the x-axis to F, then the adjacent component is Fx = F cos i and the perpendicular component is Fy = F sin i. Check with a simple case: at i = 0°, Fx = F and Fy = 0; at i = 90°, Fx = 0 and Fy = F. Always state the angle's reference axis, because swapping sin and cos gives the wrong pair. Components can be recombined using Pythagoras' theorem and trigonometry.
What earns the marks
- Resolving replaces a single vector by two perpendicular components with the same combined effect.
- For angle i measured from the x-axis, the adjacent component is Fx = F cos i.
- The perpendicular component is Fy = F sin i.
- The components are perpendicular, so they can be treated independently.
- A limiting-case check (i = 0° or i = 90°) confirms which ratio belongs to which axis.
Common mistakes and how to put them right
Swapping the ratios so that Fx = F sin i and Fy = F cos i.
Put it right: The component adjacent to the stated angle uses cos i.
Using the wrong angle, such as the angle to the y-axis, without adjusting the ratios.
Put it right: Identify the reference axis first.
Treating components as extra forces that add to the original magnitude.
Put it right: The components replace the original vector, not add to it.
Exam tips
- Sketch the right-angled triangle and label the angle before choosing sin or cos.
- Check the result at 0° and 90° to confirm the component assignment.
- State the axis from which the angle is measured in your working.
Try the lesson
The start of the Scalars and vectors: (d) resolving a vector into two perpendicular components; F x = F cos i ; F y = F sin i . lesson, made from checked teaching notes for this specification point.
Listen
Resolving splits one vector into two perpendicular components that together have the same effect. Draw the vector F as the hypotenuse of a right-angled triangle, with the two components along chosen perpendicular axes. If the angle i is measured from the x-axis to F, then the adjacent component is Fx = F cos i and the perpendicular component is Fy = F sin i. Check with a simple case: at i = 0°, Fx = F and Fy = 0; at i = 90°, Fx = 0 and Fy = F. Always state the angle's reference axis, because swapping sin and cos gives the wrong pair. Components can be recombined using Pythagoras' theorem and trigonometry. A strong answer earns marks for these points. Resolving replaces a single vector by two perpendicular components with the same combined effect. For angle i measured from the x-axis, the adjacent component is Fx = F cos i. The perpendicular component is Fy = F sin i. The components are perpendicular, so they can be treated independently. Exam tip: Sketch the right-angled triangle and label the angle before choosing sin or cos.
Key words
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Vector resolution
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Perpendicular components
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Independence of perpendicular directions
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See every definition
- Vector resolution
- Splitting one vector into two perpendicular components that together have the same effect, replacing the original vector rather than adding to it.
- Perpendicular components
- The two parts along chosen perpendicular axes that replace a single vector and can be treated independently.
- Independence of perpendicular directions
- Because the components are perpendicular, they can be treated independently, and they can be recombined using Pythagoras' theorem and trigonometry.
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