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n physics, measure of the turning effect, or torque, produced by a force acting on a body. It is equal tothe product of the force and the perpendicular distance from its line of action to the point, or pivot, abouwhich the body will turn. The turning force around the pivot is called the moment. Its unit is the newtonmetre.

The moment of a force can be worked out using the formula: moment = force applied perpendiculardistance from the pivot. If the magnitude of the force is Fnewtons and the perpendicular distanceis dmetres then:

moment = Fd

It is easier to undo a bolt using a long spanner than a short spanner. This is because more turning forceis produced at the bolt (pivot) with less effort. A long spanner is an example of a force multiplier.

In a simple balanced see-saw, the forces acting on the left- and right-hand sides of the pivot are thesame. This is known as balancing moments. Moving the load at one end will cause the see-saw tobecome unbalanced. To regain balance, the load on the opposite side must either be increased or itsposition changed. This is known as the principle of moments.

The application of balancing a moment of force (or a turning force) is used by a rope walker. By holdingthe pole in the middle the rope walker is balancing the turning force on either side of the rope. As therope walker moves a leg, the turning force on one side is greater and becomes unbalanced. To regainthe balance, the pole is shifted to balance the turning forces on both sides of the rope.moment about O = F l

where: other definitio

symbol description type units

moment effort bivector Nm=newton-metre=kg*m /s

F Force vector N=newton=kg*m/s

l perpendicular distance from pivot vector m

moment = F y

A moment is a force multiplied by the perpendicular distance from a pivot or falcrum, the units of a moment are

Newton-metres (N m). For equilibrum:

moments clockwise = moments anticlockwiseExampleFind the reactions of the beam shown:

Take moments about R1, for equilibrium,

http://www.euclideanspace.com/physics/other/standards/index.htmhttp://www.euclideanspace.com/physics/other/standards/index.htm

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moments clockwise = moments anticlockwise2500*1 + 5000*7 = R2*10

R2 = 3750N

forces acting down = forces acting up

2500 + 5000 = R1 + 3750R1 = 3750 N

One force on its own isn't much use to us. We normally look at situations where turning effects are balanced (o

not!).

Let's look at the example below and find the missing force F:

If the system is balanced, the anticlockwise turning effect of force F must equal the clockwise turning effect:

clockwise moment = anticlockwise moment

Clockwise moment = 5 N 050 m = 250 Nm.

Anticlockwise moment = F 025 m = 250 Nm

Force F = 250 Nm 025 m = 10 N

In order to balance the 5 N force acting at 05 m from the pivot, we require 10 N acting in the opposite direction

but at 025 m.

Principle of Moments

The principle of moments states that when in equilibrium the total sum of the anti clockwise moment isequal to the total sum of the clockwise moment.When a system is stable or balance it is said to be in equilibrium as all the forces acting on the systemcancel each other out.

In equilibriumThis principle can be explained by considering two people on a seesaw.

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Moments Acting On A Seesaw

Both people exert a downward force on the seesaw due to their weights.Person As weight is trying to turn the seesaw anticlockwise whilstperson Bs weight is trying to turn the seesaw clockwise.Person As Moment = Force x perpendicular distance from fulcrum

1000 x 1 = 1000 Nm

Person Bs Moment = Force x perpendicular distance from fulcrum 500 x 2 = 1000 Nm

Persons As moment = Persons Bs MomentAnticlockwise moment = Clockwise moment

Therefore seesaw is in equilibrium.

The Principle of Moments

The Principle of Moments: for a body in equilibrium (blalnced!) the sum of the

clockwisemoments is equal to the sum of the anticlockwise moments.

clockwise moments = anticlockwise moments

Garfield has considerably more weight than Odie - so for them to 'teeter-totter' Odie has to sit

a bigger distance away from the fulcrum. To play 'see-saw' their moments have to be equal

(according to the Princlple of Moments):

F1d1= F2d2

As Odie has less weight (force) he needs more distance!

How to tackle questions:

http://www.cyberphysics.co.uk/topics/forces/moments.htmhttp://www.cyberphysics.co.uk/topics/forces/moments.htmhttp://www.cyberphysics.co.uk/topics/forces/moments.htmhttp://www.cyberphysics.co.uk/topics/forces/moments.htm

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o Draw a diagramand mark on all of the information you have

been given and allocate the unknown a symbol (usually F or

d) - in an examination annotate the one on the paper.

o Identify the 'pivot point', 'turning point' or fulcrum- the point

around which the whole system turns.

o Identify all of theforcesacting.

If they act through the support you can ignore them

(as the support will produce a reaction force that willcancel them out!)

You may have to calculate some of the forces as they

may not be given to you - you may be given 'mass'

instead of weight, for example.

o Calculate the perpendicular distancefrom each of the forces

to the turning point - in advanced level questions you are

rarely given the correct distance!

o Work out all of the clockwise momentsand add them

together

o Work out all of the anticlockwise momentsand add them

together

o State the Principle of Moments

o Equatethe clockwise and anticlockwise moments

o Find the unknown

o Check that this unknown is actually the value you are asked

for in the question - sometimes they ask you for a distance

that requires this information before you can do the last step!

o Check that you have included the correct unit in your answer

and that it is to the correct number of significant figures.