Resultant Force Vector Calculator With Acceleration

Newton's Second Law:

\[ \vec{F_r} = m \times \vec{a} \]

Mass (m):

Acceleration X-component (a_x):

m/s²

Acceleration Y-component (a_y):

m/s²

Acceleration Z-component (a_z):

m/s²

Resultant Force X-component (F_x):

Resultant Force Y-component (F_y):

Resultant Force Z-component (F_z):

Resultant Force Magnitude (|F|):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Newton's Second Law?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.

2. How Does the Calculator Work?

The calculator uses Newton's Second Law:

\[ \vec{F_r} = m \times \vec{a} \]

Where:

\( \vec{F_r} \) — Resultant force vector (N)
\( m \) — Mass of the object (kg)
\( \vec{a} \) — Acceleration vector (m/s²)

Explanation: The calculator computes the force components by multiplying the mass with each acceleration component, then calculates the magnitude of the resultant force vector.

3. Importance of Force Calculation

Details: Calculating resultant forces is essential in physics and engineering for understanding motion, designing structures, analyzing mechanical systems, and predicting object behavior under various forces.

4. Using the Calculator

Tips: Enter mass in kilograms and acceleration components in m/s². All values must be valid (mass > 0). For 2D problems, set the z-component to zero.

5. Frequently Asked Questions (FAQ)

Q1: What if I only have magnitude of acceleration?
A: You'll need to know the direction components to calculate the force vector. For magnitude-only calculations, use F = m × a.

Q2: Can this calculator handle negative values?
A: Yes, negative values represent direction opposite to the positive coordinate axis.

Q3: What units should I use?
A: Use kilograms for mass, meters per second squared for acceleration, and newtons for force.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on Newton's Second Law, assuming classical mechanics applies.

Q5: Can I use this for rotational motion?
A: No, this calculator is for linear motion. For rotational motion, you need to consider torque and moment of inertia.