Physics · Class 11

Resolve a force

Rectangular components are the projections of a vector onto perpendicular axes. With θ measured from +x, the adjacent projection is F cos θ and the opposite projection is F sin θ. The force equals the vector sum of those components. Rotating through a quadrant changes component signs.

Open the interactive experiment →

One force. Two independent components.

திசையனைச் செங்குத்தான இரு அச்சுகளில் பிரிக்கலாம். +x அச்சிலிருந்து கோணம் அளந்தால் Fₓ = F cos θ, Fᵧ = F sin θ. கூறுகளின் குறிகள் அவற்றின் திசையைக் காட்டுகின்றன.

Key notes, relationships and model limits

Key relationship

Fₓ = F cos θ; Fᵧ = F sin θ; F = √(Fₓ² + Fᵧ²).

Remember

Common trap

The cosine belongs to the component adjacent to the stated angle. It is not always the horizontal component if the angle is defined differently.

Model limits

A force is resolved along perpendicular fixed axes. θ is measured from positive x, not from y. Components are signed; a negative component points along the negative axis.

What you will learn

Resolve a force; identify signs by quadrant; reconstruct its magnitude.

Try the experiment

Rotate the force through 90° and 120°. Observe when each component is zero or negative.

Think of it this way

A diagonal pull can be described as one horizontal pull and one vertical pull acting together.

Worked example

At F=50 N, θ=30°: Fₓ≈43.30 N and Fᵧ=25 N. √(43.30²+25²)≈50 N.

Why this matters

Independent component equations simplify mechanics while retaining the geometry of the original force.

Before you start

Rectangular axes · Pythagoras · sine and cosine

Check your understanding

A 10 N force is at 120° from +x. What is Fₓ?

+5 N
−5 N
+10 N

Read the explanation

Fₓ = 10 cos120° = −5 N. The arrow is in the second quadrant, so its horizontal component points left.

Course connection: CBSE XI Motion in a Plane; NEET/JEE kinematics. Use the assumptions stated in each question.