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

3. Objectives: After completing this module, you should be able to: Define and give examples of the terms torque, moment arm, axis, and line of action of a force.Define and give examples of the terms torque, moment arm, axis, and line of action of a force. Draw, label and calculate the moment arms for a variety of applied forces given an axis of rotation.Draw, label and calculate the moment arms for a variety of applied forces given an axis of rotation. Calculate the resultant torque about any axis given the magnitude and locations of forces on an extended object.Calculate the resultant torque about any axis given the magnitude and locations of forces on an extended object.

4. Torque is Determined by Three Factors: The magnitude of the applied force.The magnitude of the applied force. The direction of the applied force.The direction of the applied force. The location of the applied force.The location of the applied force. The magnitude of the applied force.The magnitude of the applied force. The direction of the applied force.The direction of the applied force. The location of the applied force.The location 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   Location of force The forces nearer the end of the wrench have greater torques. 20 N

5. Line 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. F1F1 F2F2 F3F3 Line of action

6. The 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. F2F2 F1F1 F3F3 d d d

7. Units for Torque Torque is proportional to the magnitude of F and to the distance d from the axis. Thus, a tentative formula might be:  = Fd Units: N  m or lb  ft 60 cm 40 N  = (40 N)(0.60 m) = 24.0 N  m, cw  = 24.0 N  m, cw

8. Direction of Torque 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.

9. Sign Convention for Torque By convention, counterclockwise torques are positive and clockwise torques are negative. Positive torque: Counter-clockwise, out of page cw ccw Negative torque: clockwise, into page

10. Calculating 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 Torque = force x moment arm

11. Example 1: An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque. Extend line of action, draw, calculate r.  = (80 N)(0.104 m) = 8.31 N m r = 12 cm sin 60 0 = 10.4 cm

12. Alternate: An 80-N force acts at the end of a 12-cm 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 positive 12 cm

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