2D Equilibrium Conditions

This assessment tool evaluates your understanding of the conditions required for static equilibrium of rigid bodies in two dimensions.

Background

A rigid body is in equilibrium when it remains at rest or moves with constant velocity (no acceleration). For this to occur in 2D, specific conditions must be satisfied.

The Three Equilibrium Conditions

1. Force Equilibrium in X-Direction

The sum of all forces in the horizontal direction must equal zero:

$\Sigma F_x = 0$

2. Force Equilibrium in Y-Direction

The sum of all forces in the vertical direction must equal zero:

$\Sigma F_y = 0$

3. Moment Equilibrium

The sum of all moments (torques) about any point must equal zero:

$\Sigma M = 0$

Key Concepts

• Force: A push or pull that tends to cause linear motion
• Moment (Torque): A force that tends to cause rotation about a point
• Free Body Diagram: A diagram showing all forces acting on a body

Why All Three Conditions?

Each condition prevents a different type of motion:

• $\Sigma F_x = 0$ prevents horizontal acceleration
• $\Sigma F_y = 0$ prevents vertical acceleration
• $\Sigma M = 0$ prevents angular acceleration

All three must be satisfied simultaneously for true equilibrium. If any condition is violated, the body will accelerate in that direction or rotation.

Application Steps

1. Draw a free body diagram showing all forces
2. Choose a coordinate system (x-y axes)
3. Resolve forces into x and y components
4. Apply the three equilibrium equations
5. Solve for unknown forces or reactions

Example Forces in Equilibrium

Common forces encountered in 2D equilibrium problems include:

• Weight (W): Acts downward at the center of gravity
• Normal forces (N): Act perpendicular to surfaces
• Friction forces (f): Act parallel to surfaces
• Tension forces (T): Act along cables or ropes
• Applied forces (F): External forces at specified angles