1. What is Static Equilibrium?

Definition: A system is in static equilibrium when the sum of all forces and the sum of all torques acting on it are zero.

Purpose: These conditions ensure that an object is either at rest or moving with constant velocity (no acceleration).

2. The Equilibrium Equations

The two fundamental conditions for static equilibrium:

Where:

• \( \Sigma F \) — Vector sum of all forces (Newtons, N)
• \( \Sigma \tau \) — Vector sum of all torques (Newton-meters, N·m)

Explanation: Both conditions must be satisfied simultaneously for true static equilibrium.

3. Importance of Equilibrium Analysis

Details: Essential for structural engineering, mechanical design, and understanding how objects remain stable under various forces.

4. Using the Calculator

Tips: Enter the net force and net torque values. The calculator will check if they're within a small tolerance of zero (accounting for floating-point precision).

5. Frequently Asked Questions (FAQ)

Q1: What if my system isn't in equilibrium?
A: This means your system will experience acceleration (from unbalanced forces) or rotation (from unbalanced torques).

Q2: How precise does the balance need to be?
A: The calculator uses a tolerance of 0.001 N and 0.001 N·m to account for floating-point precision.

Q3: Do these equations work in 3D space?
A: Yes, but you need to consider all three force components (x, y, z) and all three torque components.

Q4: What's the difference between static and dynamic equilibrium?
A: Static equilibrium means no motion at all, while dynamic equilibrium means constant velocity (no acceleration).

Q5: How do I calculate torque?
A: Torque = force × lever arm (perpendicular distance from pivot point to force line of action).