MOMENTS What is moments? A force can cause many things to move or stop. When a force causes an object to turn, this turning effect is called moments. Example: A person sitting on a see-saw.

Types Of Moments There are 2 types moments:  Clockwise moment  Anticlockwise moment

Everyday Examples 1. turning a door knob 2. opening a door 3. scissors 4. turning a steering wheel 5. crane at the construction sites lifting objects 6. electrical fan

Everyday Examples 7.spanner & nut

Everyday Examples Wheelbarrow

Activity  Stand up and support your bag with your wrist.  Straighten your hand. Lift it up slowly until it is perpendicular to your body.  Is it easy to do that?  Hang the bag at your elbow and repeat the motion.  How do you feel now? How do you think the distance between the pivot and the force affect the moments?

Activity  Stand up and support your bag with your wrist.  Straighten your hand. Lift it up slowly until it is perpendicular to your body.  Ask your partner to remove some books from your bag.  How do you feel as the books are removed?  What does it tell you about the relationship between force and moments?

What does the turning effect of a force depend on? 1. force 2. perpendicular distance between force and pivot

Your turn! Try out the question in the notes on how you should hang your clothes on a bamboo.

Turning Effect of a Force  Note: turning effect = moment = torque  The moment of a force is its turning effect about a pivot

Turning Effect of a Force Moments is the product of the force and the perpendicular distance from the pivot to the line of action of the force. d

CALCULATING MOMENTS Moment = force  perpendicular distance between force and pivot In symbols: Moments = F  d Weight => F d Unit for moments: Newton-metre (Nm)

F = 20N d = 3m Example 1: A cat of weight 20N stands on one end of a see-saw and the distance between the cat and the pivot is 3m, find the moment. Solution: In this case the cat is causing a clockwise moment. Clockwise moment = F x d = 20 x 3 = 60 Nm Worked Example 1

Example 2: A duck stands on one end of a see-saw, 5m away from the pivot. If the weight of the duck is 10N, find the moment. Solution: The duck ’ s weight is causing an anticlockwise moment. Anticlockwise moment= F x d = 10 x 5 = 50 Nm F = 10N d = 5m Worked Example 2

Try out the questions in the notes to find the moments caused by the force Your turn!

It is easy to balance two objects of the same weight  Anticlockwise moment  Anti- clockwise moment Anticlockwise moment Clockwise moment

Is it possible to balance a objects of different weight?

weight Principle of Moments For an object to be in equilibrium(stable/not moving), the total clockwise moment must be equal to the anticlockwise moment about the same pivot. pivot It is the fixed(non moving) point

SOLVING PROBLEMS RELATED TO PRINCIPLE OF MOMENTS Step 1: Identify what are the forces that will give rise to clockwise / anticlockwise moment Step 2: Find the clockwise / anticlockwise moment Step 3: Equate the clockwise and anticlockwise moments

10 N 30 N 6m d Find the value of d. Worked Example 3

Step 1: Identify what are the forces that will give rise to clockwise / anticlockwise moment

10 N 30 N 6m d Find the value of d. Anticlockwise moment Clockwise moment Worked Example 3

Step 2: Find the clockwise / anticlockwise moment

10 N 30 N 6m d Clockwise moment = Force x distance between force and pivot = 30 x d = 30d Nm Anticlockwise moment Clockwise moment Anticlockwise moment= Force x distance between force and pivot = 10 x 6 = 60 Nm Find the value of d. Solution: Worked Example 3

Step 3: Equate the clockwise and anticlockwise moments

10 N 30 N 6m d Find the value of d. Solution: Clockwise moment = Force x distance between force and pivot = 30 x d = 30d Nm Anticlockwise moment= Force x distance between force and pivot = 10 x 6 = 60 Nm Using the principle of moments, Clockwise moment = Anti-clockwise moment 30d = 60 d = 60  30 d = 2 m Anticlockwise moment Clockwise moment Worked Example 3

Points to note: 1.The unit for force must be in Newtons, the unit for distance must be in metres. 2.The distance must measured perpendicularly from the force to the pivot.

 The figure shows a uniform rod of length 4 m and weight 50N. It is pivoted at Q. A boy tries to lift up the rod vertically from the end P. What is the magnitude of the force when P is just lifted ? rod Q 4m Force, F P 50 N Worked Example 4

 The figure shows a uniform rod of length 4 m and weight 50N. It is pivoted at Q. A boy tries to lift up the rod vertically from the end P. What is the magnitude of the force when P is just lifted ? Solution When the body is in equilibrium, F x 4m = 50N x 2m  F = 25 N rod Q 4m Force, F P 50 N Worked Example 4

 The light ruler in the figure shown below is balanced. Calculate (a) the value of W (b) the normal reaction at the pivot P. W4N1N P 20cm15 cm 25 cm Worked Example 5

 The light ruler in the figure shown below is balanced. Calculate (a) the value of W (b) the normal reaction at the pivot P.  Solution (a) When the body is in equilibrium, (Wx20cm) = (4Nx15cm) + (1Nx40cm) therefore W = 5N (b) Normal reaction at P = ( ) = 10 N W4N1N P 20cm15 cm 25 cm Worked Example 5

Your turn! Try out the question in the notes on principle of moments