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Moments

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Tutor: Lex

Summary

Moments

In a nutshell

A force applied to an object can cause a turning effect, this turning effect is called a moment. The point around which the rotation happens is called the pivot.


Equations

WORD EQUATION

SYMBOL EQUATION

moment=force×distancemoment = force \times distance ​​
M=F×dM = F \times d​​


Variable definitions

QUANTITY NAME

SYMBOL

UNIT NAME

UNIT

momentmoment​​
MM​​
newtonmetrenewton-metre​​
NmNm​​
forceforce​​
FF​​
newtonnewton​​
NN​​
distancedistance​​
dd​​
metremetre​​
mm​​



Moment calculations

A moment is the turning effect of a force, it depends on both the size of the force being applied and the distance which is normal to the direction of force. In other words, this is the perpendicular distance between the line of action of the force and the pivot. The line of action is the line along which the force acts, so the perpendicular distance is at right angles to the line of action of the force. 


The size of a moment can be calculated using the following formula.


moment=force×distancemoment = force \times distance​​


M=F×dM = F \times d​​


As force is measured in newtons and distance in metres; moments are measured in newton-metres, NmNm​.



Example

If a child is sat at one end of a seesaw, what is the moment generated by their weight if they are sat 2 m2 \space m away from the pivot and they weigh 300 N300 \space N?


First write out the quantities needed and make sure they are in the correct for,:


f=300 Nd=2 m f=300\,N\newline d=2\,m \space


Next, write down the equation you need to use:


moment=force×distancemoment = force \times distance

​​

Then, substitute the values into the equation: 


Moment=300×2=600Moment = 300 \times 2 = 600


Don't forget to include your units: 


600 Nm600\,Nm​​


300 N300\,N child sat on a see-saw 2 m2\,m away from the pivot has a moment of 600 Nm\underline{600\,Nm}.



Principle of moments

Sometimes objects can become balanced about their pivot, this happens when the clockwise moments equal the anti-clockwise moments. The clockwise moments will cause a clockwise turning effect, and the anti-clockwise moments will cause a turning effect in the opposite direction. This means that the object balances out in both directions and experiences no overall turning effect. 


For an object in balance, the principle of moments holds:


total anticlockwise moments=total clockwise momentstotal \space anti-clockwise \space moments = total \space clockwise \space moments​​


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FAQs - Frequently Asked Questions

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