# Static equilibrium force and moment relationship

If a given object is in static equilibrium, both the net force and the net torque on the If the net moment of inertia about an axis is zero, the object will have no. We can show that there is no resultant force by adding the three forces using situation shown in Fig.3 to derive some mathematical relationships. Consequently, for true equilibrium in a static system, there must be no resultant force and no. law; buoyancy forces are governed by laws describing hydrostatic forces in fluids. Some of these . relationship is known as Hooke's law and can be expressed as an equation k. F δ = Resultant moment exerted by a force system.

**Torque: Crash Course Physics #12**

The size of the forces involved and the directions in which they act are important factors. Consideration must also be given to the position of the point through which these forces act if stability is to be ensured.

In this unit we will look at the mathematical rules governing balanced systems.

### Moments and Turning Forces

Equilibrium of forces From Newton's First Law, we know that if an object is stationary the forces acting on it must be balanced.

Drag the green dot to increase force F3 in Fig. In one investigation with the set up shown in Fig. Which one of the following shows possible values for F1 and F2?

## 14. Moments and equilibrium

F1 and F2 both equal 9 N F1 and F2 both equal 10 N F1 and F2 both equal 15 N For the point at the centre of the forces to be stationary there must be no unbalanced force in the horizontal direction. For the point at the centre of the three forces in Fig. When this happens the system is described as being in equilibrium.

Increasing the value of F3 increases the values of F1 and F2 required for equilibrium. Click through the stages in Fig. Forces in equilibrium The point at the centre of the forces is acted on by three forces.

We can show that there is no resultant force by adding the three forces using the rules of vector addition. In the animation of Fig. F2 is then added to F3 remembering to keep its size and direction correct. We consider only forces that act up or down.

### Moments and equilibrium - Mechanics

The distance from the point where the force acts to the axis is called the moment arm, d1 and d2 in the diagram. The product of the force times the moment arm is called the torque also called the momentand is represented by the Greek letter tau: It is positive by convention if it tends to rotate the object in a counter-clockwise direction around the axis.

It is negative if it tends to rotate the object in a clockwise direction around the axis. In the diagram the torque due to F2 is positive and the torque due to F1 is negative. The forces themselves have signs. We may take forces positive if directed up, and negative down.

The conditions for equilibrium are then stated simply: The sum of all forces must be zero, and the sum of all torques must be zero. One particular force requires further consideration: The weight force of earth's gravity does not act at a point, but acts at all points along the object. However, for purposes of determining equilibrium, the weight can be considered to be concentrated at a single point, called the center of mass.

Thus, a bar supported by two upward forces, and held in equilibrium, looks like the figure below.