TorqueTorque► Consider force Consider force

required to open door. required to open door. Is it easier to open the Is it easier to open the door by door by pushing/pulling pushing/pulling awayaway from hinge or from hinge or closeclose to to hinge?hinge?

closeclose to hinge to hinge

awayaway from from hingehinge

Farther Farther from from from from hinge, hinge, larger larger rotational rotational effect!effect!

Physics concept: Physics concept: torquetorque

TorqueTorque

► TorqueTorque, , is the , , is the tendency of a forcetendency of a force to rotate an object about some axisto rotate an object about some axis

is the torqueis the torque dd is the is the leverlever arm arm (or (or momentmoment arm) arm) FF is the force is the force

Fd

Door example:

Lever ArmLever Arm

► The lever arm, d, The lever arm, d, is the is the shortest shortest (perpendicular)(perpendicular) distance from the axis distance from the axis of rotationof rotation to a line to a line drawn along the the drawn along the the direction of the forcedirection of the force

d = L sin Φd = L sin Φ

► It is It is not necessarilynot necessarily the the distance between the distance between the axis of rotation and axis of rotation and point where the force is point where the force is appliedapplied

Direction of TorqueDirection of Torque

► Torque is a vector quantityTorque is a vector quantity The direction is The direction is perpendicularperpendicular

to the to the planeplane determined by determined by the the lever armlever arm and the and the forceforce

Direction and sign: Direction and sign: If the turning tendency of the If the turning tendency of the

force is force is counterclockwisecounterclockwise, the , the torque will be positivetorque will be positive

If the turning tendency is If the turning tendency is clockwiseclockwise, the torque will be , the torque will be negativenegative

Direction of torque: out of page

UnitsUnits

SISI Newton meter (Nm)Newton meter (Nm)

US CustomaryUS Customary Foot pound (ft lb)Foot pound (ft lb)

An Alternative Look at An Alternative Look at TorqueTorque

► The force could also be The force could also be resolved into its resolved into its x- and x- and y-componentsy-components The x-component, The x-component, F cos F cos

ΦΦ, produces , produces 0 torque0 torque The y-component, The y-component, F sin F sin

ΦΦ, produces a non-zero , produces a non-zero torquetorque

sinFLF is the forceF is the force

L is the distance along the objectL is the distance along the object

Φ is the angle between force and objectΦ is the angle between force and object

LL

ConcepTest 1ConcepTest 1

You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If you instead tie a rope to the doorknob and then pull with the same force, is the torque you exert increased? Will it be easier to open the door?

1. No2. Yes

ConcepTest 1ConcepTest 1

You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If you instead tie a rope to the doorknob and then pull with the same force, is the torque you exert increased? Will it be easier to open the door?

1. No2. Yes

ConcepTest 2ConcepTest 2

You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is most effective in loosening the nut? List in order of descending efficiency the following arrangements:

ConcepTest 2ConcepTest 2

You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is most effective in loosening the nut? List in order of descending efficiency the following arrangements:

2, 1, 4, 3 or2, 4, 1, 3