Moment : the turning effect of a force about a pivot

Moments depend on two factors :

Moment = Force x perpendicular distance.

Moment = Force x distance Calculate the moment of a 20N force a distance of 1.2m from the pivot. Moment = Fd = 20 x 1.2 = 24Nm

Examples of different pivots

In equilibrium When a plank is balanced, it is perfectly horizontal When a plank is balanced it is not horizontal

In equilibrium, the total clockwise moments are equal to the total anticlockwise moments.

I f the moments are not equal, the rod will not be in equilibrium and will tilt . Cw moment = Fd = 6 x 50 = 300Nm Acw moment = Fd = 4 x 80 = 320Nm the acw moment is larger, so the rod will tilt acw!

Problems involving moments If a rod is in equilibrium, The total cw moments = the total acw moments Fd = Fd F x 8 = 20 x 12 8F = 240 F = 240 8 F = 30N

Practice A uniform rod is in equilibrium. What is the force needed to keep it in balance ? In equilibrium Total cw moment = total acw moment W x 20 = 2 x 10 20W = 20 W = 1N

Important words Pivot : the point about which the turning occurs In equilibrium : balanced Uniform rod: its centre of gravity is at the centre Negligible weight : its weight is not taken into consideration.

More than 2 forces: First mark the cw and the acw moments. Then use the same law of moments: In equilibrium Total cw moments = total acw moments 3xd + 1 x 40 = 2 x 50 3d+ 40 = 100 3d = 100-40 3d = 60 d = 20cm

practice First mark the cw and acw moments. In equilibrium Total cw moments = total acw moments 20 x 1.5 + 100 x 1.2 = 50 x 2.5 + F x 3.7 30 + 120 = 125 + 3.7F 150 = 125 + 3.7F 150 – 125 = 3.7F 25 = 3.7F F = 6.76N

Forces acting at the pivot. In a system in equilibrium, there are forces which are usually not taken into consideration. These are the weight and the reaction. These are a distance of 0 from the pivot This means that they produce a moment of 0. Forces acting at the pivot produce NO MOMENT

To find the reaction force, you need to know the other forces. If the weight of the seesaw is 5kg, what is the reaction at the pivot? In equilibrium Total upward forces = total downward forces. R = 600 + 200 + 50 ( always remember to convert Kg into Newtons. R = 850N

A uniform rod of weight W is balanced at the centre on a pivot A uniform rod of weight W is balanced at the centre on a pivot. If the reaction is 35N, what is the weight of the rod? Total upward forces = total downward forces 35 = W + 20 + 10 35 = W + 30 W= 5N