Question

What is the moment? Give an example.

Answer 1

Hint: Recall that a moment of a force is nothing but the effect on an unopposed applied force along a direction different than its line of action on an object pivoted about an axis. Determine the kind of motion that such an object would execute, given that it is hinged on one side, and consequently arrive at an example for the same by employing the principle of moments.

Formula Used:
$Moment\;=\; Force \times Perpendicular\;distance$

Complete answer:
Moment, or moment of a force, is generally defined as the tendency of the force to cause a body to rotate about a specific point or axis. It is quantitatively given as:
$Moment\;=\; Force \times Perpendicular\;distance$
This is different from the tendency of a body to move or translate in the direction of the applied force and this applied force acts on the body in such a way that it causes the body to rotate about a pivot. Thus, the moment is the turning effect of a force around a fixed point called a pivot. Such a motion occurs every time when the applied force does not have an equal and opposite force to counter it along its line of action.
A moment is also defined with a directional sense. A clockwise rotation about the pivot will be a positive moment and the anticlockwise rotation about the pivot will be considered to be negative.
This leads us to the principle of moments which suggests that when a system is balanced the total sum of the anti-clockwise moments will be equal to the sum of the clockwise moment. This means that when a system is stable or in balance, it is said to be in equilibrium as all the forces acting on the system cancel each other out and no rotational motion occurs.
Let us look at an example.
Suppose two people are pushing on a door from opposite sides. The pivot will be the hinges of the door. If both are pushing with an equal force then there will be no rotation due to equilibrium. This is a consequence of the principle of moments. But if one of them was to suddenly back off from the door, then the push of the other person would no longer be opposed and the door would rotate and swing about the hinge. Thus, a moment is created when there is no opposing force in the direction of the applied force.
Additionally, the further away the applied force is from the hinge of the door, the greater is the turning effect. This is also why doorknobs are placed on the side opposite to the hinges of a door. This maximizes the perpendicular distance between the hinge (pivot) and the doorknob (applied force), which in turn maximizes the distance through which the door turns and opens even if a small force is applied. However, if you apply the same amount of force closer to the hinges, the door doesn’t turn as much since the perpendicular distance between the hinge and the applied force is reduced, thereby reducing the moment caused by the force.

Note:
In the above discussion, we confined ourselves to the moment of a force (which is sometimes called torque). However, moment can be defined for any physical quantity and is the product of the quantity and its perpendicular distance from the origin of its predefined coordinate system. For example, angular momentum is the 1st moment of momentum. (But the linear moment itself is not a moment). Similarly, the total mass is the 0th moment of mass. The centre of mass is the 1st moment of mass, and the moment of inertia is the 2nd moment of mass. Thus, moments essentially describe the rotational analogues of linear quantities.