Measure of the turning effect, or torque, produced by a force acting on a body. It Is equal to the product of the force and the perpendicular distance from Its line of action to the point, or pivot, about which the body will turn. The turning force around the pivot is called the moment. Its unit is the Newton meter. The moment of a force can be worked out using the formula: moment = force applied x perpendicular distance from the pivot.
If the magnitude of the force is F Newton’s and the perpendicular distance is d meters then: moment = FDA It is easier to undo a bolt using a long spanner than a short spanner. This is because more turning force is 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 the same. This is known as balancing moments. Moving the load at one end will cause the see-saw to become unbalanced.
To regain balance, the load on the opposite side must either be Increased or Its position 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 alike. By holding the pole in the middle the rope walker Is balancing the turning force on either side of the rope. As the rope walker moves a leg, the turning force on one side is greater and becomes unbalanced. To regain the balance, the pole is shifted to balance the turning forces on both sides of the rope. Moment about O = F where: other definitions symbol description type units moment effort blotter Force vector N=Newton=keg*m/so perpendicular moment = F y Allocates Trot pivot A moment is a force multiplied by the perpendicular distance from a pivot or fulcrum, he units of a moment are Newton-meters (N m). For equilibrium: moments clockwise = moments anticlockwise Example Find the reactions of the beam shown: Take moments about RI, for equilibrium, moments clockwise = moments anticlockwise 2500*1 + 5000*7 = RE*10 RE = NEON forces acting down = forces acting up 2500 + 5000 = RI + 3750 RI = 3750 N One force on its own isn’t much use to us.
We normally look at situations where turning effects are balanced (or 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 he clockwise turning effect: clockwise moment = anticlockwise moment Clockwise moment = 5 N x 0;50 m = 2;50 Nm. Anticlockwise moment = F x 0;25 m = 2;50 Nm Force F = 2;50 Nm m = 10 N In order to balance the 5 N force acting at m from the pivot, we require 10 N acting in the opposite direction but at 0;25 m.
Principle of Moments The principle of moments states that when in equilibrium the total sum of the anti clockwise moment is equal 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 system cancel each other out. In equilibrium This principle can be explained by considering two people on a seesaw. 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 whilst person Bi’s weight is trying to turn the seesaw clockwise. Person As Moment = Force x perpendicular distance from fulcrum 1000 x 1 = 1000 Nm Person Bi’s Moment = Force x perpendicular distance from fulcrum 500 x 2 = 1000 Persons As moment = Persons Bi’s Moment Anticlockwise moment = Clockwise moment Therefore seesaw is in equilibrium. The Principle of Moments The Principle of Moments: for a body in equilibrium (balanced! ) the sum of the clockwise moments is equal to the sum of the anticlockwise moments. Likewise moments = anticlockwise moments Garfield has considerably more weight than Edie – so for them to ‘teeter-totter’ Edie has to sit a bigger distance away from the fulcrum. To play ‘see-saw’ their moments have to be equal (according to the Principle of Moments): Fall = Fad As Edie has less weight (force) he needs more distance! How to tackle questions: Draw a diagram and mark on all of the information you have been given and allocate he unknown a symbol (usually F or d) – in an examination annotate the one on the paper.
Identify the ‘pivot point’, ‘turning point’ or fulcrum – the point around which the whole system turns. Identify all of the forces acting. If they act through the support you can ignore them (as the support will produce a reaction force that will cancel 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. Calculate the perpendicular distance from each of the forces to the ruining point – in advanced level questions you are rarely given the correct distance!
Work out all of the clockwise moments and add them together Work out all of the anticlockwise moments and add them together State the Principle of Moments Equate the clockwise and anticlockwise moments Find the unknown 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! Check that you have included the correct unit in your answer and that it is to the correct number of significant figures.
