1. Torque and Equilibrium
Physics 12

3. Dynamics Extension – Part I
Learning Outcome (Student will…):
 use vector analysis in two dimensions for systems involving two or more masses, relative motions, static equilibrium, and static torques

4. Two Types of Equilibrium
1. Translational Equilibrium
2. Rotational Equilibrium

5. Translational Equilibrium
Definition: Static - not moving
Definition: Translate - to move through space without rotating
Definition: Translational Equilibrium - the condition where the vector sum of all forces acting on a body is 0 N or...
Definition: Statics - the branch of physics that deals with the calculation of forces acting on bodies which are in equilibrium

6. Rotational Equilibrium
Definition: Torque - the product of the lever (or moment) arm and the applied force
angle between the object and the line along which the force acts
“tau”
lever arm or  from the line along which the force acts to the point of rotation
force
measured in Nm
every force on an object contributes a torque!

7. Definition: Static Equilibrium – a state where an object is in both translational and rotational equilibrium

9. Torque
In the past we have looked at forces that have acted through the centre of mass of an object
These leads to forces that will act against each other but not result in a net torque on an object
This leads to an object that is either at equilibrium or accelerating but everything is linear Ff Fa FN Fg

10. Torque
We will now decouple forces so that forces may act at a distance from the centre of mass
This can result in a net torque which will result in the object twisting due to the applied forces Ff Fa FN Fg

11. Torque
Torque is calculated as the product of the applied force and the distance away from a pivot point that the force is applied
The pivot point is often the centre of mass but may be chosen to be another point based upon the question
If a system is at equilibrium, the net torque and net force must be equal to zero

12. Torque m1 m2
Fg1
Fg2 r1 r2

13. Torque As torque is a vector, it must have direction
When a product is used, the direction must be perpendicular to both vectors used in the product
The direction will be determined using the right hand thumb rule
Thumb out of the board is positive, thumb into the board is negative

14. Torque m1 m2 Fg1 Fg2 r1 r2 This will result in positive torque
This will result in negative torque
At equilibrium, the net torque would be equal to zero

15. Torque Example
Two masses are placed on a seesaw of length 2.0m with the fulcrum in the middle. The first mass is 10.kg and the second mass is 15kg. If the first mass is placed so that its mass acts through the end of the seesaw, where must the second mass be placed?

16. Torque Example
Two masses are placed on a seesaw of length 2.0 m with the fulcrum in the middle. The first mass is 10.0 kg and the second mass is 15.0 kg. If the first mass is placed so that its mass acts through the end of the seesaw, where must the second mass be placed? m2
Fg1
Fg2 r1 r2 m1

17. Torque Example

18. Torque Example 2
2 people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N. If one person applies an upward force of 60.0 N at one end of the board, where must the other person be standing in order for the board to be in static equilibrium and with what force must they apply?

19. Step 1 – Sum of the Forces
F2=?
F1=60.N
Fg=160N

20. Step 2 - Torque
F2=100N
F1=60.N
r2=?
r1=1.50m
Fg=160N

21. Ladder Question
A painter (mass = 75kg) stands 2.0m up a 3.0m ladder with a mass of 15kg. The ladder makes an angle of 60.° with the ground and there is no friction between the ladder and the wall.
What force does the wall apply to the ladder?
What is the minimum coefficient of friction that must exist between the ladder and the ground?

22. Ladder Problem
FNw Fw
Fgp FN
Fgl Ff

23. Ladder Problem

24. Ladder Problem

25. Practice Problems
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