Moment the turning effect of a force about

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 20 N force a distance of 1. 2 m from the pivot. Moment = Fd = 20 x 1. 2 = 24 Nm

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 = 300 Nm Acw moment = Fd = 4 x 80 = 320 Nm the acw moment is larger, so the rod will tilt acw!

Problems involving moments

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 20 W = 20 W = 1 N

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 3 xd + 1 x 40 = 2 x 50 3 d+ 40 = 100 3 d = 100 -40 3 d = 60 d = 20 cm

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. 7 F 150 – 125 = 3. 7 F F = 6. 76 N

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 5 kg, 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 = 850 N

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