Moments – Turning Forces
Moments are often called turning forces. They are the product of the distance a force is acting from the point being considered and the component of the force acting perpendicular to the direction.
The most common example of moments used in on a see saw. Here there a two levers, each side of the see saw, acting from the central pivot. if a person sits on the see saw there is a moment about the pivot because of there weight. While the seesaw is still horizontal this moment is the product of their weight (mass times gravity) and the distance they are still from the pivot because the distance a long the see saw to the pivot is perpendicular to their weight.
Like forces if something is in equilibrium, velocity isn’t changing (usually but not always at rest), the moments have to be balanced. Because moments are turning forces this means that all the moments acting clockwise have to equal all the moments acting anti clockwise. This means that if two people are sitting on the seesaw provided the product of their weight and distance is the same the seesaw wont turn, even if one person is much heavier than the other. For example if a heavy person sits close to the centre they can be balanced by a light person sitting further away.
Just to note – moments don’t have to be calculated about a pivot or turning point, they can be found about any point, so we cud take them about one of the people or the end of the seesaw. IF you do this though, remember that the pivot is providing an upward force on the seesaw that is equal to its mass plus that of the two people times gravity. This sort of method can often be useful in more complex systems as by taking moments about a point then we can ignore all forces acting through it (as their distance is 0) and simplify our equations.
However we can also calculate the moments caused by forces that aren’t perpendicular to their distance, for example the moment cause by the person on the seesaw when it is titled or on the ground. Here we have to find the component of the force that is in the direction that is perpendicular to the distance, by resolving using sin and cos.
This is done by multiplying the product either by the sin of the angle between force and the direction of the distance between the force and pivot or the cos of the angle between them force and the direction perpendicular to the distance.
for example if the seesaw is tilted by 30 degrees from the horizontal we can have to multiply by
cos(30)=sin(60) =√3 /2
By David Woodford,
If you have any questions please leave them in comments below or email me at david.woodford.4@googlemail.com
Excelent explanation, but it is still to be stressed that basically the moment is defined as the multiplication between a force with it’s lever respect to the pivot point. By this definition, the readers understand why both of sine and cosine functions can involve on the moment expression.
Apologise Mr.Rohedi, Denaya is now more interested to the expression of √3, cos we’ve just celebrated the square root day on 3/3/9. Would you help @Dave in getting the value of √3 by simple way?
Of course @Dave, like for pi number we are imposible to write square root of a number in fractional form. Denaya believes Dave still remember that world has Calandra method as the simpliest method for calculating square root. Unfortunately Calandra method is still difficult to get the root of 3, even it can’t gives the root of 4.
Denaya, 4=2*2, so mr.Dave need not Calandra method to calculate the square root of 4, coz it is equal 2, isn’t it?.
I think Denaya’s comment is correct, because the Calandra method is always based on finding a number that has nearest square but still smaller than the number that to be calculated it’s square root. So, for square root of 4, the Calandra method yeilds 1.999999… not precise 2.
root 3 can be proved to be irrational so im unsure what you mean by getting the value of root 3 as it cant be written as a fraction or finite/recurring decimal.
though I would be glad to help
dave,