Turning effect of forces

A moment is the turning effect of a force around a pivot. Moments play a crucial role in everyday life and engineering, influencing how objects rotate and remain in balance. Understanding how forces cause rotation helps in designing stable structures, machines, and tools.

What is a moment

A moment occurs when a force is applied to an object in such a way that it causes it to rotate about a fixed point, known as a pivot or fulcrum. The size of the moment depends on two factors:

1. The force applied (N).

2. The perpendicular distance from the pivot to the force (m).

Examples of Moments in Everyday Life

• Opening a Door – Pushing near the handle (far from the hinge) requires less effort than pushing near the hinge.

• Using a Wrench – A longer wrench allows more leverage, making it easier to turn a bolt.

• A See-Saw – A heavier person sitting closer to the pivot can balance a lighter person sitting farther away.

• Turning a Steering Wheel – The larger the wheel, the less force is needed to turn it.

Moment of a force equation

Moment of a Force Equation

The moment of a force is calculated using the formula:

Moment = Force × Perpendicular Distance from Pivot

Units:

• Moment: Newton-meters (Nm)

• Force: Newtons (N)

• Distance: Meters (m)

Example Calculation

A force of 50 N is applied at a distance of 0.4 m from a hinge.

Moment = 50 × 0.4 = 20 Nm

• A greater force or a larger distance from the pivot increases the moment.

• If the force acts perpendicularly, the moment is maximized.

The principle of moments

For an object to be in balance (rotational equilibrium), the sum of clockwise moments must equal the sum of anticlockwise moments.

∑Clockwise Moments = ∑Anticlockwise Moments

Where ∑ (sigma) represents "sum of".

Example: Balancing a Beam

A 3 m long beam is supported at the center.

• A 30 N force is applied 1.2 m to the left.

• What force is needed 1.5 m to the right to balance it?

30 × 1.2 = F × 1.5

F = 30 × 1.2/1.5 = 24N

• If the moments on both sides of the pivot are equal, the beam stays balanced.

Equilibrium

An object is in equilibrium if:

1. No resultant force – It remains stationary or moves at a constant speed.

2. No resultant moment – It is not rotating.

Example: Ladder Leaning Against a Wall

• A ladder resting against a wall is in equilibrium if all forces (gravity, reaction forces) and moments are balanced.

• If the forces are not balanced, the ladder tips over.

More complex moment calculations

In cases where multiple forces act on each side of the pivot, the principle of moments still applies:

∑Clockwise Moments = ∑Anticlockwise Moments

Example: A Plank Supported at Both Ends

A 2 m plank is supported at two points.

• A 60 N force acts 0.5 m to the left.

• A 40 N force acts 1.5 m to the right.

Find the reaction forces at the supports.

• By applying the principle of moments at different pivot points, we can determine the reaction forces at each support.

Experimenting with moments