1. Turning effect of a force 1 pivot problems 2 pivot problems
Moments
Turning effect of a force
1 pivot problems
2 pivot problems

2. Moment of a force Moment is the turning effect of a force.
This can be increased by:
Increasing the force.
Increasing the distance from the force to the pivot

3. Definition
Moment = Force x perpendicular distance from force to pivot m = Fdcosθ

4. Units
Since it is product of force and distance then the unit of moment is Nm or Ncm as appropriate.

5. Principle of moments
For equilibrium The sum of the anticlockwise moments is equal to the sum of the clockwise moments. The net force vertically is zero.

6. Example
Show that this system is in equilibium

7. acwm = cwm 500 N x 2 m = 1000N x 1 m 1000 Nm = 1000Nm

8. Example
A shelf of width 50 cm and weight 10 N is attached to a wall and supported by a strut 80 cm long. A book of weight 15 N is placed on the shelf so that its centre of mass is 20 cm from the wall.
The total moment of the downward forces.
The force in the strut.

10. Total moment clockwise = 15x x25 = 550 Ncm Therefore total moment provided by strut is also 550 Ncm Fdsinθ = 550

11. θ is between the 50 and 80 cm lengths

12. cos θ = 50/80 θ = 51. 3 degrees Fx50xsin(51. 3) = 550 F = 14
cos θ = 50/80 θ = 51.3 degrees Fx50xsin(51.3) = 550 F = 14.1 N The force in the support strut is N

13. Two pivot problems
Bridge 2 men carrying a ladder

14. Example
A ladder of length 5m and mass 10 kg is carried by two men. A supports the ladder at the left hand end and B supports it 1 m from the right hand end. Find the force each exerts on the ladder (the support forces.)

15. Diagram is vital

16. Answer Take moments about A acwm = cwm 10x9.8x2.5 = F(B)x4 = F(B)x4
61.25 N = F(B)
F(A) + F(B) = 10x9.8  F(A) = N

18. Torque
Turning effect of a pair of forces Cars – peak torque advertised and at a known rev range – more torque = more responsive to throttle dabs. Power is a function of both torque and cycles per unit time.