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Vertical component of a force Formula, SPM Physics

Formula: F_y = F sin θ. Not given in the exam, recall it.

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Vertical component of a force
F_y = F sin θ

Not given in the exam, recall it.

What it is for

Vertical component of a force is used in Force and Motion II (SPM Physics Form 5). Keep the SI units in every line of working. Force and Motion II

Symbols and SI units

SymbolMeaningSI unit
F_yvertical component of forceN
FforceN
θangle to the horizontal°

Rearrangements

  • F = F_y / sin θ
  • sin θ = F_y / F

Worked example

A force F = 50 N acts at θ = 30° to the horizontal. F_y = F sin θ = 50 × sin 30° = 50 × 0.5 = 25 N.

Common trap

Use sin for the component opposite the angle (usually vertical). Measure θ from the horizontal.

Understanding the vertical component of a force

The formula F_y = F sin θ resolves a force into its vertical part. F_y is the vertical component in newtons (N). F is the full force, also in newtons. θ is the angle to the horizontal, in degrees (°).

Sine appears because the vertical side is opposite the angle. As θ increases, sin θ increases, so more of the force acts vertically, a force pointing steeply upward lifts strongly but drags forward only weakly.

Rearrange when needed: F = F_y / sin θ recovers the full force, and sin θ = F_y / F gives the angle. Keep the calculator in degree mode and measure θ from the horizontal, so that a large angle correctly produces a large vertical component.

A worked example, step by step

A cable pulls a load with force F = 200 N at θ = 25° to the horizontal. Find the vertical component that helps lift the load.

Apply the formula with units:

  • F_y = F sin θ = 200 N × sin 25°
  • F_y = 200 N × 0.423 = 84.5 N

So the upward part of the pull is F_y = 84.5 N (3 significant figures). This is the share that reduces the load's effective weight on the ground.

Check: because 25° is a shallow angle, sin 25° is small, so F_y (84.5 N) is much less than F (200 N). Most of the force here acts horizontally, which matches the small angle.

Common mistakes and how this is tested

The main trap: use sin for the component opposite the angle (usually vertical), and measure θ from the horizontal.

Other common errors:

  • Swapping sin and cos, giving the horizontal component instead.
  • Forgetting that weight (mg) may add to or oppose F_y in equilibrium problems.
  • Using radian mode, so sin 25° is wrong.

Questions ask you to calculate the vertical component, to define the resolution of a force into perpendicular components, or to explain how the vertical component affects the normal reaction or apparent weight.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026

Frequently asked questions

Is this formula given in the exam?
No. SPM Physics papers provide no formula sheet, so this must be recalled.
When is the vertical component largest?
When θ = 90°, the force points straight up and sin 90° = 1, so F_y = F. The whole force then acts vertically and none of it drags the object horizontally.
How does F_y affect the normal reaction?
An upward F_y reduces how hard the object presses on the ground, so the normal reaction falls. This is why pulling a lawnmower at an angle can lighten it on the grass.
Why use sine for the vertical part?
The vertical side of the right-angled triangle is opposite the angle θ measured from the horizontal, and sine relates the opposite side to the hypotenuse (the full force F).

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