TorqueTorqueTorque is defined as the tendency to produce a change in rotational motion.

Torque is defined as the tendency to produce a change in rotational motion.

Torque is a Torque is a twist or turn twist or turn that tends to that tends to produce produce rotation. * * * rotation. * * * Applications Applications are found in are found in many common many common tools around tools around the home or the home or industry where industry where it is necessary it is necessary to turn, tighten to turn, tighten or loosen or loosen devices.devices.

Objectives: After completing Objectives: After completing this module, you should be this module, you should be able to:able to:

• Define and give examples ofDefine and give examples of the terms the terms torque, moment arm, axis, torque, moment arm, axis, andand line of line of action action of a force. of a force.

• Draw, label and calculate the Draw, label and calculate the moment moment armsarms for a variety of applied forces given for a variety of applied forces given an axis of rotation.an axis of rotation.

• Calculate the Calculate the resultant torqueresultant torque about any about any axis given the magnitude and locations of axis given the magnitude and locations of forces on an extended object.forces on an extended object.

Torque is Determined by Three Torque is Determined by Three Factors:Factors:

• The The magnitudemagnitude of the applied force. of the applied force.

• The The directiondirection of the applied force. of the applied force.

• The The locationlocation of the applied force. of the applied force.

• The The magnitudemagnitude of the applied force. of the applied force.

• The The directiondirection of the applied force. of the applied force.

• The The locationlocation of the applied force. of the applied force.

20 N

Magnitude of force

40 N

The 40-N force produces twice the torque as does the

20-N force.

Each of the 20-N forces has a different

torque due to the direction of force. 20 N

Direction of Force

20 N

20 N20 N

Location of forceThe forces nearer the

end of the wrench have greater torques.

20 N20 N

Units for TorqueUnits for TorqueTorque is proportional to the magnitude of F and to the distance d from the axis. Thus, a tentative formula might be:

Torque is proportional to the magnitude of F and to the distance d from the axis. Thus, a tentative formula might be:

= Fd = Fd Units: Nm or lbft

60 cm

40 N

= (40 N)(0.60 m)

= 24.0 Nm, cw

= 24.0 Nm, cw = 24.0 Nm, cw

Direction of TorqueDirection of Torque

Torque is a vector quantity that has direction as well as magnitude.

Torque is a vector quantity that has direction as well as magnitude.

Turning the handle of a screwdriver clockwise

and then counterclockwise will

advance the screw first inward and then outward.

Sign Convention for Sign Convention for TorqueTorque

By convention, counterclockwise torques are positive and clockwise

torques are negative.Positive torque:

Counter-clockwise, out of

pagecw

ccw

Negative torque: clockwise, into page

Line of Action of a ForceLine 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.

The line of action of a force is an imaginary line of indefinite length drawn along the direction of the force.

F1

F2

F3Line of action

The Moment ArmThe Moment Arm

The moment arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation.

The moment arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation.

F2

F1

F3

d

dd

Calculating TorqueCalculating Torque

• Read problem and draw a rough figure.Read problem and draw a rough figure.

• Extend line of action of the force.Extend line of action of the force.

• Draw and label moment arm.Draw and label moment arm.

• Calculate the moment arm if necessary.Calculate the moment arm if necessary.

• Apply definition of torque:Apply definition of torque:

• Read problem and draw a rough figure.Read problem and draw a rough figure.

• Extend line of action of the force.Extend line of action of the force.

• Draw and label moment arm.Draw and label moment arm.

• Calculate the moment arm if necessary.Calculate the moment arm if necessary.

• Apply definition of torque:Apply definition of torque:

= Fd = Fd Torque = force x moment arm

Example 1:Example 1: An An 80-N80-N force acts at the end of force acts at the end of a a 12-cm12-cm wrench as shown. Find the torque. wrench as shown. Find the torque.

• Extend line of action, draw, calculate r.

= (80 N)(0.104 m) = 8.31 N m

= (80 N)(0.104 m) = 8.31 N m

r = 12 cm sin 600 = 10.4 cm

r = 12 cm sin 600 = 10.4 cm

Alternate:Alternate: An An 80-N80-N force acts at the end of force acts at the end of a a 12-cm12-cm wrench as shown. Find the torque. wrench as shown. Find the torque.

Resolve 80-N force into components as shown.

= (69.3 N)(0.12 m) = 8.31 N m as before = 8.31 N m as before

positive

12 cm