Physics Tutorial 6.4 - Moment of Force. Conditions of Equilibrium Revision Notes

In these revision notes for Moment of Force. Conditions of Equilibrium, we cover the following key points:

• What is moment of force?
• What are the factors affecting the moment of force?
• What is the equation and unit of moment of force?
• What happens if the acting force is not normal to the bar?
• What happens if more than two forces are acting on a turning system?
• What happens if there is no equilibrium in a turning system?
• What if the bar is heavy and as such, we cannot neglect its weight?
• What if the bar is hanged on a string?
• Which are the two conditions of equilibrium?

Moment of Force. Conditions of Equilibrium Revision Notes

When a system tends to rotate around the pivot or the hanging point, a turning effect towards the support is produced. In scientific terms, this turning effect is known as "Moment of Force", in short M⃗ and it is a vector quantity.

There are two possible turning directions in such systems: clockwise and anticlockwise.

There are two factors affecting the turning effect (moment) of a force. They are:

1. The magnitude of force

Greater the force, easier the rotation around the turning point, i.e. greater the moment of force.

2. The distance from the turning point

Greater the distance from the turning point, easier the rotation around the turning point, i.e. greater the moment of force.

Combining the above factors in a single equation, we obtain for the Equation of moment of force:

where F⃗_⊥ is the perpendicular force to the bar, which acts on it and ∆x⃗ is the linear distance from the application point of the force to the turning point (pivot) of the bar.

"A system which tends to rotate around a fixed point is in equilibrium only when its clockwise moment of force is equal to the anticlockwise one."

This means the clockwise turning effect of one force is balanced by the anticlockwise turning effect of the other force.

Mathematically, we can write:

Or,

If any of the acting force is not normal to the bar, we consider only the force component that lies normal to the bar as only it contributes in the rotation of the system. The other component, i.e. the component of force according the direction of the bar, goes in vain, as it gives no contribution in the rotation.

If there are more than two forces acting on such a system, first we determine the direction of rotation of each force. This is because they may be on the same side of the bar but act in opposite directions. Then we use the equation of moments of force.

If the system is not in equilibrium, it is not balanced. This means there will be a non-zero resultant moment in the direction of the greatest turning effect.

If the bar is too heavy to be neglected, we take its weight as an additional downward force exerted at the bar's centre of gravity. Then, we use the usual approach mentioned above to find any missing quantity. This is also true for systems in which a bar is hanged on a string and some objects are attached to it.

An object is in equilibrium if it tends to move linearly and the forces acting on it are balanced. Thus, if we want to set in equilibrium such an object or system, we must meet the following condition:

This is known as the first condition of equilibrium. It is valid for translational (linear) motion

On the other hand, if the system tends to rotate around a fixed point, the equilibrium is settled only when the resultant moment of force is zero, i.e. when

Or

The above equation is known as the second condition of equilibrium. It is valid for circular motion around a fixed point.