What is a Moment?
A moment is the turning force around a fixed pivot (a fixed point). Everyday examples include:
- A spanner tightening a nut
- A child on a seesaw
- A door opening on its hinge
The pivot is the fixed point around which the rotation occurs (e.g., the nut, the middle of the seesaw, the hinge).
Balanced Moments (Equilibrium)
When an object is balanced (in equilibrium), the moments acting on it are equal and opposite.
- A lighter child must sit further from the pivot to balance a heavier child.
- A heavier child must sit closer to the pivot.
The moment size depends on force (weight) and distance from pivot.
Calculating a Moment
The formula for moment is:
Moment = Force × Perpendicular Distance from Pivot
- Unit: Newton meter (Nm)
- Force: Newtons (N)
- Distance: meters (m)
Important: The distance must be the perpendicular (right-angle) distance from the pivot to the line of action of the force. For more on understanding how forces combine, see How to Calculate Resultant Forces Using Vector Diagrams.
Example 1: Balanced Seesaw
- Lighter child: 500 N at 2 m → Moment = 500 N × 2 m = 1000 Nm
- Heavier child: 1000 N at 1 m → Moment = 1000 N × 1 m = 1000 Nm
- Result: Perfectly balanced (clockwise and anticlockwise moments are equal).
Example 2: Wheel Nut
A person applies a force to tighten a wheel nut. You calculate the moment by multiplying the force (Newtons) by the perpendicular distance (in meters, not centimeters).
Correct calculation: If force is 10 N and distance is 0.3 m (30 cm), the moment is 3 Nm.
Formula Triangle
You can rearrange the moment formula using a triangle:
- M = F × d (Moment = Force × Distance)
- F = M ÷ d (Force = Moment ÷ Distance)
- d = M ÷ F (Distance = Moment ÷ Force)
Clockwise and Anticlockwise Moments
For an object to be in equilibrium (balanced):
Clockwise moments = Anticlockwise moments
Summary
- Moments are turning forces measured in Newton meters (Nm).
- They are calculated as Force × Perpendicular Distance from the pivot.
- For balance, clockwise and anticlockwise moments must be equal.
Think of a spanner loosening a fixed nut or a child on a seesaw or a door opening around a fixed hinge.
All of these things are connected by something called moments. A moment is the turning force around a
fixed pivot. The pivot is the nut or the middle of the seesaw or the hinge.
We can have one moment acting which results in a turning force. Or if something is balanced or in
equilibrium, the moments are equal and opposite. To be balanced, this lighter child needs
to sit further away from the pivot and the heavier child needs to be closer. This is because the size of a moment is
determined by the force and a distance. So the moments of the lighter person is 500 Newtons multiplied by 2 meters.
1,000 Newton meters. And the heavier person is 1,000 * 1 meter to also give 1,000 Newton meters.
They're perfectly balanced on their seesaw. Did you notice that moments are measured
in Newton meters, NM, because force is measured in Newtons, N, and distance in meters?
Note that the distance must be the perpendicular distance from the pivot to force.
Here's another example. Can you work out what moments the woman is applying to tighten the wheel nut?
Pause the video and work it out. Did you get 3 Newton meters? Were you careful to change the 30
centimeters into meters? We can also place this formula into a formula triangle.
Force equals moments divided by distance. Distance equals moments divided by
force. And moments, as we already know, is force * distance.
Here are two more questions for you to try. Pause the video and work them out. Did you get both questions right?
For this seesaw, we do actually say clockwise moments and anti-clockwise moments. And for something to be
balanced, the clockwise and anti-clockwise moments must be equal. So, there we have moments. They're
measured in Newton meters and are the force multiplied by the perpendicular distance.
A moment is the turning effect of a force around a fixed point called the pivot. Common examples include a spanner turning a nut, a child on a seesaw, or a door opening on its hinge. The size of the moment depends on both the force applied and the perpendicular distance from the pivot.
The moment is calculated using the formula: Moment = Force × Perpendicular Distance from the pivot. The force must be measured in newtons (N) and the distance in meters (m) to get the moment in newton meters (Nm). For example, a 10 N force applied 0.3 m from a pivot gives a moment of 3 Nm.
The distance must be measured perpendicularly because only the component of the force acting at right angles to the lever arm produces the turning effect. If you measure along the line of action, you would overestimate or underestimate the actual turning force. This ensures the calculation reflects the true rotational force about the pivot.
Balanced moments occur when the clockwise and anticlockwise moments are equal, causing the seesaw to be in equilibrium. For example, a lighter child (500 N) sitting 2 m from the pivot creates a 1000 Nm moment, which balances a heavier child (1000 N) sitting 1 m away. In this state, the moments are equal and opposite, and no rotation occurs.
It means the turning forces are in equilibrium, so the object does not rotate. The total clockwise moment equals the total anticlockwise moment. This condition is necessary for any object to be balanced around a pivot, such as a seesaw, a lever, or a spanner tightening a nut to the correct torque.
You can rearrange the moment formula using a triangle: M = F × d, so Force = Moment ÷ Distance, and Distance = Moment ÷ Force. For example, if you know the moment is 100 Nm and the force is 20 N, the distance is 100 ÷ 20 = 5 m. This is useful when solving for an unknown variable.
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