4.1 Turning Effects of Forces

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1. Centre of Gravity

What is the centre of gravity?

The centre of gravity of an object is the single point where we can consider all of the object's weight to act.

Think of it this way: even though an object's weight is spread throughout its entire body, we can treat it as if all that weight is concentrated at one special point. This makes calculations much simpler.

Where is the centre of gravity located?

For symmetrical objects with uniform density (objects that have the same material throughout and are evenly shaped), the centre of gravity is at the point of symmetry (the geometric centre).

Examples:

• For a uniform sphere (like a ball), the centre of gravity is at its centre
• For a uniform rectangular block, it's in the middle
• For a uniform ruler, it's at the 50 cm mark (halfway along)
• For a person standing upright, it's roughly in the middle of the body, behind the navel

Important notes:

• The centre of gravity doesn't have to be inside the object's material – it can be outside. For example, a ring's centre of gravity is in the empty space in the middle.
• The centre of gravity can change position if the object changes shape. When you lean forward, your centre of gravity moves forward too.
• Centre of gravity vs centre of mass: In a uniform gravitational field (like on Earth's surface), these two points are in the same place. The centre of mass depends only on how the object's mass is distributed, while the centre of gravity depends on the gravitational field. In space near large bodies like Earth, they can be in slightly different positions.

2. Moment of a Force

What is a moment?

A moment is the turning effect of a force. When you apply a force to something that can rotate around a fixed point (called a pivot or fulcrum), you create a moment.

Think about opening a door: when you push on the door handle, you're creating a moment that makes the door rotate around its hinges. The hinges are the pivot.

The moment formula:

moment = F × d

Where:

• moment is measured in newton metres (N m)
• F is the force in newtons (N)
• d is the perpendicular distance from the pivot to the line of action of the force, measured in metres (m)

What does "perpendicular distance" mean?

This is crucial: the distance must be measured at right angles (90°) to the direction of the force.

Here's a helpful way to remember:

• If the force is vertical (up or down), measure the horizontal distance
• If the force is horizontal (left or right), measure the vertical distance

Example 1: Simple moment calculation

A force of 20 N is applied vertically downward at a point 0.5 m from a pivot. What is the moment?

Solution:

• F = 20 N
• d = 0.5 m (perpendicular distance)
• moment = F × d = 20 × 0.5 = 10 N m

When the force is at an angle:

Sometimes the force isn't applied perpendicular to the distance from the pivot. In this case, you need to find either:

• The component of the force that acts perpendicular to the distance, OR
• The component of the distance that is perpendicular to the force

Example 2: Force at an angle

A force of 100 N acts at an angle of 60° to a 1.2 m rod that is pivoted at one end. Calculate the moment.

Solution:

We need the component of force that acts perpendicular to the rod.

Using trigonometry:

• Perpendicular component of force = 100 × sin(60°) = 100 × 0.866 = 86.6 N
• Distance along the rod = 1.2 m
• moment = 86.6 × 1.2 = 104 N m

Note: The component 100 cos(60°) acts along the rod toward the pivot and produces no turning effect.

Important principle:

A force produces no moment about a pivot if its line of action (the imaginary line along which the force acts) passes through the pivot. This is because the perpendicular distance would be zero.

Real-life application:

Door handles are placed far from the hinges (the pivot) to maximize the distance 'd' for a given force. This creates a larger moment, making it easier to open the door with less effort.