The moment of a force, also known as the torque, is a measure of the turning effect of a force. It quantifies how effective a force is at causing rotation around a pivot point. It depends on the magnitude of the force, the perpendicular distance from the line of action of the force to the pivot point (the perpendicular distance), and the angle between the force and the perpendicular distance.

The formula for the moment of a force is:

Moment = Force x Distance x sin(angle)

The factors that affect the magnitude of the moment are:

• Magnitude of the force: A larger force will produce a larger moment, assuming the distance and angle remain constant.
• Perpendicular distance: A larger perpendicular distance from the line of action of the force to the pivot point will produce a larger moment, assuming the force and angle remain constant.
• Angle between the force and the perpendicular distance: The moment is maximum when the force is perpendicular to the distance. The moment is zero when the force is parallel to the distance (sin(0°)=0).

Example: Consider a person using a crowbar to lift a heavy stone. The person applies a force to one end of the crowbar, and the crowbar acts as a lever with the pivot point (fulcrum) located closer to the stone. The distance from the fulcrum to where the person applies the force is much greater than the distance from the fulcrum to the stone. This large distance, combined with the force applied, creates a large moment. This large moment overcomes the large turning effect of the stone, allowing the person to lift it. Without the crowbar (or a similar lever), the force required to lift the stone would be much greater.

Moment = Force × Perpendicular Distance

Force = 50 N

Perpendicular Distance = 1.5 m

Moment = 50 N × 1.5 m = 75 Nm

Answer: The moment of the force is 75 Nm.

Solution:

The principle of moments applies here. Torque is calculated as Force x Distance from the pivot (hinge).

Torque = 50 N x 0.5 m = 25 Nm

The torque on the door is 25 Nm.