Any single vector can be split into two perpendicular components
Scalars & Vectors - OCR A-Level Physics
- Any single vector can be split into two perpendicular componentsThe two perpendicular parts (horizontal and vertical) that a single vector can be resolved into..
- This is the reverse of adding vectors -- it is called resolvingSplitting a single vector into two perpendicular components, typically horizontal and vertical..
- Choose two perpendicular directions (usually horizontal and vertical, or parallel and perpendicular to a slope).
- The horizontal component acts along the x-axis.
- The vertical component acts along the y-axis.
- The angle theta is measured between the vector and the direction you want the component in.
$$F_x = F\cos\theta$$
$$F_y = F\sin\theta$$
- Memory aid: cos goes with the component closest to the angle. sin goes with the component that is sideways from the angle.
- Always draw a right-angled triangle showing the vector and its two components.
- Check: F_\(x^{2}\) + F_\(y^{2}\) should equal \(F^{2}\) (Pythagoras).
Common Mistake
MEDIUM
Wrong: Swapping sin and cos when resolving. Using F sin(theta) for the component adjacent to the angle.
Right: The component ADJACENT to the angle always uses cos. The component OPPOSITE to the angle always uses sin. Draw the triangle and label the angle to avoid this error.
Right: The component ADJACENT to the angle always uses cos. The component OPPOSITE to the angle always uses sin. Draw the triangle and label the angle to avoid this error.
Examiner Tips and Tricks
- If the angle is given from the vertical (not the horizontal), cos and sin swap roles.
- F cos(theta) gives the vertical component and F sin(theta) gives the horizontal.
- Always check which direction the angle is measured from.