1. Torque

2. Torque / Moment ~ Turning Force
e.g. the force used to open a door d F
Torque (or moment) is a vector:
By convention, counter clockwise torques are positive and clockwise torques are negative.
Units for torque are Nm
The Pivot point (or fulcrum) is the point around which the object rotates.

3. Ex: A meter stick
45 cm
Find the Torque exerted on the meter stick due to the 50 g mass that is suspended from it.

4. Ex: The torque on a door ℓ
 = F ℓ

5. Line of Action of a Force
The line of action of a force is an imaginary line of indefinite length drawn along the direction of the force. F2 F1 F3
Line of action

6. The moment arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation. F1 r F2 F3 r r

7. Example: An 80-N force acts at the end of a 12-cm wrench as shown
Example: An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque.
Extend line of action, draw, calculate r.
= (80 N)(0.104 m)
= N m
r = 12 cm sin = 10.4 cm

8. Alternate: An 80-N force acts at the end of a 12-cm wrench as shown
Alternate: An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque.
positive
12 cm
Resolve 80-N force into components as shown.
Note from figure: rx = 0 and ry = 12 cm
t = (69.3 N)(0.12 m)
t = 8.31 N m as before

9. Static Torque Dynamic Torque
Is when the torques acting produce a change in rotational motion.
Static Torque
Is when the torques acting add together (?) or cancel out, to ensure an object is stationary (rotationally obeys Newton’s 1st Law).

10. Dynamic Torque -
Movement

11. Static –
Stationary

12. contact force of pivot
weight of stand
The point on an object where all its weight seems to be concentrated is called the centre of mass (or gravity).

13. An object in Equilibrium means…
contact force of pivot
weight of stand
weight of mass
An object in Equilibrium means…

14. If these conditions are met, we say that something is in Equilibrium.
F=ma If F = 0 then a = 0
=I If  = 0 then  = 0
If these conditions are met, we say that something is in Equilibrium.
Fx = 0
Fy = 0
 = 0
the total of all the anti- clockwise torques
the total of all the clockwise torques =

15. St = 0 Example: Is the seesaw in this picture balanced?
B: Moment = Force x distance
= 600 N x 1.5 m
= 900 Nm
A: Moment = Force x distance
= 500 N x 2 m
= 1000 Nm
No, the seesaw is not balanced. It will turn anticlockwise.

16. The mass of the boy and the tray is 65 kg.
Show the mass of the plank is 11 kg
Take g = 9.8 m s-2
5 m
2.5 m
F1 = 370 N
740 N
F2 = 370 N

17. The support forces and the weight forces are balanced.
5 m
2.5 m
F1 = 370 N
740 N
F2 = 370 N
The mass of the boy and the tray is 65 kg.
Show the mass of the plank is 11 kg
Take g = 9.8 m s-2
The support forces and the weight forces are balanced.
The upward forces = downward forces
370 N N = weight of the boy + weight of plank
740 N = 637 N N
Weight = mass x gravity mass = 103/9.8 = 10.5
mass = 11 kg (2sig.fig)
Students succeed better in Physics when answers that require calculations:
Show all working i.e., equation, substitution and answer. (Criterion 2);
Have correct significant figures (Criterion 1); and
Show the correct unit (Criterion 1)

18. Show the mass of the 1 m ruler is about 200 g. Take g = 9.8 m s-2
The weight of the ruler Fw acts at the centre 0.5 m from the end.
The support force is labeled Fs
1 m
0.1 m
0.5 m
15 N
0.05 m Fs

19. Take moments about the support force Fs.
Show the mass of the 1 m ruler is about 200 g. Take g = 9.8 m s-2
The weight of the ruler Fw acts at the centre 0.5 m from the end.
The support force is labeled Fs
0.1 m
0.5 m
15 N
0.05 m Fs
Fw (ruler)
Take moments about the support force Fs.

20. The plank has a weight of 98 N.
The boy and tray have a weight of 637 N.
How far to the left (d) of the fulcrum (FLS) can the boy stand without the plank tipping?
5.0 m
0.40 m d
Fw = 98 N
FB = 637 N
FLS
2.5m
FRS = 0
Take moments about FLS

21. Torques in the Arm

22. The angle at which this man’s back is bent places an enormous force on the disks at the base of his spine, as the lever arm for FM is so small.

23. Given: W=50 N, L=0.35 m, x=0.03 m
Find the tension in the muscle W x L

24. Problems with TWO Pivot points
Consider the 400-kg beam shown below. Find TR

25. An man walks across a shark infested creek
An man walks across a shark infested creek. The mass of the bridge is 45 kg and is 5.2 m long. A man of mass 85 kg tentatively walks to a point 1.3 m from end A to get a better view of the sharks below. The man is unaware that termites have weaken support B so that it will support only 500 N. Does the man get wet? B A
1.3 m
5.2 m
At what point does he get wet?