Static equilibrium refers to a state where a body is at rest or moving at a constant velocity. For a body to be in static equilibrium under the action of forces, two conditions must be satisfied:

1. The vector sum of all forces acting on the body must be zero. This is also known as the equilibrium condition for forces. Mathematically, it can be represented as ∑F = 0. This means that the body is not accelerating and is either at rest or moving at a constant velocity.

2. The sum of all torques (moments) acting on the body about any point must also be zero. This is also known as the equilibrium condition for torques or moments. Mathematically, it can be represented as ∑τ = 0. This means that the body is not rotating.

Now, let's discuss these conditions for both coplanar concurrent and non-concurrent force systems:

A. Coplanar Concurrent Forces: In this system, all forces meet at a common point. The conditions of static equilibrium for this system are:

- The sum of all forces in the x-direction must be zero (∑Fx = 0).
- The sum of all forces in the y-direction must be zero (∑Fy = 0).
- Since all forces meet at a common point, the sum of moments is automatically zero.

B. Coplanar Non-Concurrent Forces: In this system, the forces do not meet at a common point. The conditions of static equilibrium for this system are:

- The sum of all forces in the x-direction must be zero (∑Fx = 0).
- The sum of all forces in the y-direction must be zero (∑Fy = 0).
- The sum of moments about any point must be zero (∑M = 0). This is because the forces do not meet at a common point, and hence, can create a moment or torque.

Question

Static equilibrium refers to a state where a body is at rest or moving at a constant velocity. For a body to be in static equilibrium under the action of forces, two conditions must be satisfied:

1. The vector sum of all forces acting on the body must be zero. This is also known as the equilibrium condition for forces. Mathematically, it can be represented as ∑F = 0. This means that the body is not accelerating and is either at rest or moving at a constant velocity.

2. The sum of all torques (moments) acting on the body about any point must also be zero. This is also known as the equilibrium condition for torques or moments. Mathematically, it can be represented as ∑τ = 0. This means that the body is not rotating.

Now, let's discuss these conditions for both coplanar concurrent and non-concurrent force systems:

A. Coplanar Concurrent Forces: In this system, all forces meet at a common point. The conditions of static equilibrium for this system are:

- The sum of all forces in the x-direction must be zero (∑Fx = 0).
   - The sum of all forces in the y-direction must be zero (∑Fy = 0).
   - Since all forces meet at a common point, the sum of moments is automatically zero.

B. Coplanar Non-Concurrent Forces: In this system, the forces do not meet at a common point. The conditions of static equilibrium for this system are:

- The sum of all forces in the x-direction must be zero (∑Fx = 0).
   - The sum of all forces in the y-direction must be zero (∑Fy = 0).
   - The sum of moments about any point must be zero (∑M = 0). This is because the forces do not meet at a common point, and hence, can create a moment or torque.

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