Angle Of Resultant Force Calculator

Angle of Resultant Force Formula:

\[ θ = \arctan\left(\frac{F_2 \sin(α)}{F_1 + F_2 \cos(α)}\right) \]

Angle of Resultant Force θ (degrees):

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1. What is Angle of Resultant Force?

Definition: This calculator determines the angle (θ) of the resultant force when two forces (F₁ and F₂) act on a body, with F₂ acting at an angle α to F₁.

Purpose: It helps in physics and engineering to analyze force systems and determine the direction of the net force.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ θ = \arctan\left(\frac{F_2 \sin(α)}{F_1 + F_2 \cos(α)}\right) \]

Where:

\( θ \) — Angle of resultant force (degrees)
\( F_1 \) — First force (N)
\( F_2 \) — Second force (N)
\( α \) — Angle between F₁ and F₂ (degrees)

Explanation: The formula calculates the angle of the resultant force relative to F₁ using trigonometric relationships.

3. Importance of Angle of Resultant Force

Details: Knowing the direction of the resultant force is crucial for equilibrium analysis, structural design, and motion prediction.

4. Using the Calculator

Tips: Enter both force values in Newtons and the angle between them in degrees (0-360). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What if F₁ is zero?
A: When F₁=0, θ simply equals α (the angle of F₂ becomes the resultant angle).

Q2: What range should the angle α be?
A: Typically between 0° and 360°, though angles beyond 180° represent forces acting in opposite directions.

Q3: How is this different from magnitude calculation?
A: This calculates direction only. Use the Pythagorean theorem for magnitude.

Q4: What if both forces are equal and α is 90°?
A: The resultant angle will be exactly 45° between the two forces.

Q5: Can this be used for 3D forces?
A: No, this is for 2D coplanar forces only. 3D systems require vector components in all three dimensions.