IGCSE Physics - 1.5.2 Turning Effect of Forces

This section explores the concept of the moment of a force, which quantifies the turning effect of a force. We will define moment, understand the factors affecting it, and examine everyday examples.

Moment of a Force

The moment of a force (also known as torque) is a measure of how much a force causes an object to rotate. It depends on the magnitude of the force, the perpendicular distance from the line of action of the force to the pivot point (also called the axis of rotation), and the angle between the force and the perpendicular distance.

Mathematically, the moment of a force is given by:

$$ \text{Moment} = \text{Force} \times \text{Distance} \times \sin(\theta) $$

Where:

• Force is the magnitude of the force applied (in Newtons, N).
• Distance is the perpendicular distance from the line of action of the force to the pivot point (in meters, m). This is often referred to as the lever arm.
• $\theta$ is the angle between the force and the perpendicular distance. The maximum moment is achieved when the force is perpendicular to the distance (i.e., $\theta = 90^\circ$, and $\sin(90^\circ) = 1$).

Factors Affecting the Moment

The moment of a force is affected by three main factors:

1. Magnitude of the force: A larger force will produce a larger moment, assuming the distance and angle remain constant.
2. Perpendicular distance (Lever arm): A larger perpendicular distance will produce a larger moment, assuming the force and angle remain constant.
3. Angle between the force and the perpendicular distance: The moment is maximum when the force is perpendicular to the distance. If the force is parallel to the distance, the moment is zero.

Everyday Examples

Here are some everyday examples illustrating the turning effect of forces:

1. Opening a Door

When you push or pull a door, you apply a force at a distance from the hinges (the pivot point). The further you push or pull from the hinges, the easier it is to open the door. This is because a larger distance increases the moment of the force.

2. Using a Crowbar

A crowbar is a lever designed to amplify a force. You apply a force at one end of the crowbar, and the crowbar pivots at a fixed point (the fulcrum). The distance from the fulcrum to where you apply the force is much greater than the distance from the fulcrum to the object you are trying to move. This creates a large moment, allowing you to lift heavy objects with a relatively small force.

3. Using a Wrench

When tightening or loosening a nut or bolt with a wrench, you apply a force to the handle of the wrench. The handle acts as a lever, and the nut or bolt acts as the resistance. The distance from the fulcrum (the point where the wrench touches the nut/bolt) to where you apply the force on the handle determines the moment. A longer wrench provides a greater moment, making it easier to turn the nut/bolt.

4. Ropes and Pulleys

Pulleys are used to change the direction of a force and often to reduce the amount of force required to lift an object. By using a system of ropes and pulleys, the moment of the force can be altered, making it easier to lift heavy loads.

Momentum Table

Factor	Effect on Moment
Magnitude of Force	Directly proportional - larger force, larger moment
Perpendicular Distance (Lever Arm)	Directly proportional - larger distance, larger moment
Angle between Force and Distance	Proportional to sin(θ) - maximum moment when θ = 90°