1. Moment of a Force

2. Topics Definition of Moment Sum of Moments Conditions for Equilibrium
Centre of Gravity
Couple

3. Consider this… Rotation
What happens to the wood when a force is applied at one end from the hinge?

4. Moment of a Force Rotational effect of a force
Product of force and its perpendicular distance from the pivot
M = F x d
Units: Nm

5. Perpendicular distance from the pivot
Moment of a Force
Force
pivot
Perpendicular distance from the pivot

6. Which of these forces will cause greater rotation at the hinge?
Moment of a Force
1 N
2 N
Which of these forces will cause greater rotation at the hinge?

7. Which of these forces will cause greater rotation at the hinge?
Moment of a Force
1 N
1 N
Which of these forces will cause greater rotation at the hinge?

8. What is the magnitude of the moment of each of these forces?
Moment of a Force
0.8 m
1 N
0.5 m
1 N
What is the magnitude of the moment of each of these forces?

9. Moment of a Force
Vector Quantity
Direction
Clockwise
Anticlockwise

10. In which direction will the beam rotate?
Sum of Moments
0.4 m
0.5 m
10 N
10 N
In which direction will the beam rotate?

11. What is the net moment for this beam?
Sum of Moments
0.4 m
0.5 m
10 N
20 N
What is the net moment for this beam?

12. Sum of Moments
0.5 m
0.5 m
10 N
10 N
What is the net moment for this beam?
What will happen to the beam?

13. Conditions for Equilibrium
Sum of the forces is zero in all directions
Sum of the moments is zero at any point

14. Conditions for Equilibrium
Sum of the forces in one direction is equal to the sum of the forces in the opposite directions
Sum of the clockwise moments is equal to the sum of the anticlockwise moments at any point

15. Conditions for Equilibrium

16. Sample Problem 1 What magnitude of weight will balance the seesaw?

17. Sample Problem 2 Where should the 30-N force be to balance the seesaw?x
Where should the 30-N force be to balance the seesaw?

18. Sample Problem 3
40 cm m
30 kg
30 cm
Two boys played on a seesaw. What is the mass of the other kid?

19. Centre of Gravity

20. What is meant by centre of gravity?

21. A point where the whole weight of the object may be considered to act
Centre of Gravity
A point
where the whole weight of the object
may be considered to act

22. If an object is supported at its centre of gravity, it is balanced.

23. Regularly-shaped objects
The centre of gravity is at its geometric centre.

24. The centre of gravity does not have to be on the body of the object.

25. If an object is hanged at one point, the string hangs such that the line passes through its centre of gravity.

26. Sample Problem 4
A beam is hanged between two spring balances as shown. S1 S2
80 cm

27. If Spring balance 1 reads 1 N and Spring balance 2 reads 1 N, what is the weight of the beam?
80 cm

28. Sample Problem 5
A beam is hanged between two spring balances as shown. And an orange is placed at the position shown. S1 S2
20 cm
80 cm

29. If spring balance 1 reads 2. 0 N and spring balance 2 reads 1
If spring balance 1 reads 2.0 N and spring balance 2 reads 1.0 N, what is the weight of the orange? S1 S2
20 cm
80 cm

30. What is the weight of the beam?
20 cm
80 cm

31. Couple

32. What is meant by a couple?

33. Couple
A pair of forces
That have equal magnitudes but opposite in direction
And have a turning effect about a pivot located midway between them

34. same distance from pivot
Couple is composed of
2 forces
equal magnitudes
opposite in direction
same distance from pivot
ΣF = 0 but ΣM ≠ 0

35. Exercises