TorqueTorque

TorqueTorque TorqueTorque results when a results when a forceforce acts to acts to rotaterotate an object an object A force applied to some point other than A force applied to some point other than

the center of gravitythe center of gravity To C of G To C of G TranslationalTranslational To off C of G To off C of G RotationalRotational

Leverage – torque produced when force Leverage – torque produced when force applied with leverage applied with leverage

Ex. Doorknob far away from turning axis Ex. Doorknob far away from turning axis (hinges)(hinges)

Direction of Force is perpendicular to Direction of Force is perpendicular to planeplane

TorqueTorque

Torque dependent on:Torque dependent on: 1. Distance from turning axis1. Distance from turning axis

Lever armLever arm Distance from point of contact to axisDistance from point of contact to axis

2. Perpendicular component of applied 2. Perpendicular component of applied forceforce

ττ = F d = F d ττ = Torque; F = perpendicular force; d = = Torque; F = perpendicular force; d =

distance from centerdistance from center

TorqueTorque

Three wrenches – same force Three wrenches – same force applied. Which would do the best applied. Which would do the best job?job?

11

22

33

See-sawSee-saw

Balance if torques equal.Balance if torques equal. What if not equal?What if not equal?

Meter Stick ExampleMeter Stick Example

20 cm 90 cm

50 cm

20 N ? N

Counterclockwise Torque = Clockwise Torque

Balance

A B

F┴A x DA = F┴B x DB

Coupled ForcesCoupled Forces

Two forces of equal magnitude but opposite direction in the same Two forces of equal magnitude but opposite direction in the same plane but not the same pointplane but not the same point

Pair of forces such as this is coupled:Pair of forces such as this is coupled:

The torque equals the product of one of the forces and the The torque equals the product of one of the forces and the perpendicular distance betweenperpendicular distance between

Can’t be balanced with a single force, must balance with another Can’t be balanced with a single force, must balance with another couplecouple

F

F

xA

xB

ReviewReview TorqueTorque

Produces a clockwise or counterclockwise Produces a clockwise or counterclockwise motion when a force is applied at a point motion when a force is applied at a point other than the center of gravityother than the center of gravity

ττ = F d = F d Three ConditionsThree Conditions

FFleftleft = F = Frightright

FFupup = F = Fdowndown

FFclockwiseclockwise = F = Fcounterclockwisecounterclockwise

The arrows tell you if the force is clockwise or The arrows tell you if the force is clockwise or counterclockwisecounterclockwise

Example ProblemExample Problem

100 lbs

20 lbs

40 lbs2 ft

3 ft x

Fclockwise = Fcounterclockwise