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Torque and Equilibrium. Physics 12. 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

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Torque
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

FN

Ff

Fa

Fg


Torque1
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

FN

Fa

Ff

Fg


Torque2
Torque

  • Torque is calculated as the cross 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


Torque3
Torque

m1

m1

m1

m2

m2

m2

r1

r1

r2

r2

r2

Fg2

Fg2

Fg1

Fg1


Torque4
Torque

  • As torque is a vector, it must have direction

  • When a cross 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


Torque5
Torque

m1

m2

r1

r2

Fg2

Fg1

At equilibrium, the net torque would be equal to zero

This will result in positive torque

This will result in negative torque


Torque example 1
Torque Example 1

  • Copy this down!!

  • 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 15.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 so that the net torque is zero?


Torque example
Torque Example

m2

m1

r1

r2

Fg1

Fg2


Torque example 2
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. 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?


Step 1 sum of the forces
Step 1 – Sum of the Forces

F2=?

F1=60.N

Fg=160N


Step 2 torque
Step 2 - Torque

F2=100N

F1=60.N

r2=?

r1=1.50m

Fg=160N


Example 3 ladder question
Example 3 … 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?


Ladder problem
Ladder Problem

FNw

Fw

Fgp

FN

Fgl

Ff




Practice problems
Practice Problems

  • Page 495

    • 29-30

  • Page 501

    • 31-34


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