# Moments of a Force

## Calculating Moments

When an object is made to rotate about a pivot or fulcrum the turning effect of the force is called the *moment of the force*. The moment is a way of measuring how much a force acting in a straight line results in the object turning or rotating.

Moment of a force (Nm) = force (n) x distance normal to the force to the pivot.

The last part of this equation sounds confusing. It is a way of saying the shortest distance between the point where a force acts and the pivot point. Look at the diagram of the seesaw to see what this means.

- When the seesaw is level the distance from the force (the weight of the person) to the pivot is the same as the length along the plank.

The green arrow shows the distance normal to the force to the pivot when the seesaw is level.

The orange arrow shows how this has reduced as the seesaw increases in angle.

- As the seesaw move upwards the distance normal to the force reduces.

The turning effect of a force increases as the force applied increases and as the distance between the force and the pivot increase.

**Try this:** Try pushing open the door to the room you are in by pushing on the door as far from the hinge as possible. Then try opening it by pushing on the door as close to the hinge as possible. What happens to the force you needed to use when you pushed close to the hinge?

Moment of a force example: Calculate the moment of a force of 20 N applied to a spanner handle at:

a. 10 cm from the nut

b. 25 cm from the nut

a. Moment | = force x normal distance from force to pivot |

= 20 N x 0.1 m = 2Nm | |

b. Moment | = force x normal distance from force to pivot |

= 20 N x 0.25 m = 5 Nm |

As the distance increases so does the moment of the force.

Example 2: A wheelbarrow carries a load of 100 N, what force is needed to lift this load?

Moment of the load | = force x normal distance to the pivot |

= 100 N x 0.5m | |

= 50 Nm |

The force to lift the load has to have the same moment as the load, ie. 50 Nm.

So if Moment of the force = force x normal distance to the pivot

then force | = Moment / normal distance to the pivot |

= 50 Nm / 1.5 m | |

= 33.3 N |

By applying the lifting force further from the pivot (the wheel), the force needed to lift the load is reduced.

## Moments in Equalibrium

When two different forces, or sets of forces, act upon a single object but on opposite sides of the pivot, their moments will have the opposite effects on the motion of the object.

This is the principle upon which a seesaw works. The people on either side make the seesaw rotate in opposite direction alternatively. However, an old fashioned balance for weighing qualities, in sayca kitchen, requires the system to be balanced on either side of the pivot.

In this example the system is in equilibrium, balanced. Therefore, the moment on the right hand side causing a clockwise rotation, must be balanced by the moment on the left hand side, causing an anti-clockwise rotation.

Right Hand side moment = force x distance = 200 x 1.5 = 300Nm

The force on the left to balance this is:

Force = moment / distance = 300 / 0.75 = 405.45 N

As the force is closer to the pivot on the left hand side than on the right hand side, it must be larger.

Example 2:

In this balance a 200 N weight can be moved to balance the weight applied on the right hand side. What distance will the 200 N weight have to be placed to bring the scales into equilibrium?

Moment of left hand side | = | Moment of right hand side |

Moment = force x distance | Moment = force x distance | |

Distance = moment / force | = 50 N x 0.2 m = 10 Nm | |

=10 Nm / 200 N | ||

= 0.05 m or 5 cm from the pivot |

## Levers

Levers are some of the simplest and earliest examples of simple machines acting as___ force multipliers___. A lever places a load on one side of a pivot and the effort force on the other side.

The lever works by placing the load to be moved very close to the pivot, but the effort force much further away on the opposite side of the pivot. This gives a relatively small moment on the load side, this can be balanced by a small force at a larger distance to give the same moment on both sides of the lever’s pivot point.

The smaller effort force is ‘multiplied’ by the differences in the distances on either side of the pivot. To move the load the moment on the effort side must be just slightly larger than the moment on the load side of the lever’s pivot point.

**Gears**

Gears are a set of wheels with interlocking teeth, as they rotate the drive wheel will rotate more often than the load wheel. This mean a small but faster rotating effort can produce a larger but slower rotating load. The slower rotation on the load wheel acts as a force multiplier, via the differences in rotation of the two wheels.

- Calculate the force required to just lift up the wheelbarrow in the image below.
- Your answer should include: 100N / 100

Explanation:*Moment of load = force x distance from pivot = 150 N x 0.8m = 120 Nm To just lift the load the moment of effort on the handles must at least equal the moment of the load, so it must be at least 120 Nm. As moment = force x distance from pivot, force = moment / distance from pivot Force = 120 Nm / 1.2 m = 100 N* - If a 850 N weight is applied 1.5m to the left of the pivot of a seesaw what weight must be applied to the right side of the pivot at a distance of 2m for the system to be in equilibrium.
- Your answer should include: 637.5N / 637.5

Explanation:*Left hand side Moment = force x distance = 850N x 1.5 m = 1275 Nm Right hand side moment = left hand side moment for system equilibrium. Moment = 1275 Nm Force = moment / distance = 12,750 Nm / 2 m = 637.5 N* - Explain how a lever can make it easier to remove a tyre from a bike wheel when a puncture needs to be repaired.
- smaller force

Explanation:*The lever allows the person to use a smaller force than would be needed if they had to do the same job unaided. The lever places a pivot point close to the load, which in this case is the force needed to pull the tyre over the rim of the wheel. This gives a relatively low moment on the load side of the pivot. To move the tyre the person must apply an effort force on the other side of the lever’s pivot point. The further away from the pivot the person applies the effort, the smaller the force will need to be to remove the tyre from the wheel.*