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Torque

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

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Torque

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

  2. 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.

  3. What makes something rotate in the first place? TORQUE How do I apply a force to make the rod rotate about the axis? Not just anywhere! AXIS

  4. TORQUE • To make an object rotate, a force must be applied in the right place. • the combination of force and the distance from the axis to the point of application (L) is called TORQUE. lever arm, L Axis Force, F

  5. Torque = force times lever arm Torque = F  L

  6. Torque example What is the torque on a bolt applied with a wrench that has a lever arm of 30 cm with a force of 30 N? F Torque = F  L = 30 N  0.30 m = 9 N m L For the same force, you get more torque with a bigger wrench  the job is easier!

  7. Each of the 20-N forces has a different torque due to the direction of force. Direction of Force 20 N q 20 N q 20 N Magnitude of force The 40-N force produces twice the torque as does the 20-N force. Location of force The forces nearer the end of the wrench have greater torques. 20 N 40 N 20 N 20 N 20 N Torque is Determined by Three Factors: • The magnitude of the applied force. • The direction of the applied force. • The location of the applied force.

  8. 60 cm 40 N Units for Torque Torque is proportional to the magnitude of F and to the distance L from the axis. Thus, a tentative formula might be: t = FL Units: Nm or lbft t = (40 N)(0.60 m) = 24.0 Nm, t = 24.0 Nm,

  9. Direction of Torque Torque is a vector quantity that has direction as well as magnitude. Turning the handle of a screwdriver clockwise (negative) and then counterclockwise (positive) will advance the screw first inward and then outward.

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

  11. F2 F1 F3 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. Line of action

  12. F1 F2 F3 The Moment Arm The lever arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation. L L L

  13. Calculating Torque • Read problem and draw a rough figure. • Extend line of action of the force. • Draw and label Lever arm. • Calculate the Lever arm if necessary. • Apply definition of torque: t = FL Torque = force x Lever arm

  14. Torque If we know the angle  between F and r, we can calculate torque! t = F L r is the total length F is force L = r sin   = r sin  F  is angle between F and r The SI unit of torque is the Nm. Hinge (rotates) Direction of rotation F r  L Extend the line of action

  15. Sample Problem 1 Consider the door to the classroom. We use torque to open it. Identify the following: The point of rotation. The point of application of force. The total length (r). The angle between r and F (best guess).

  16. Torque simplified Usually,  will be 90o, so then…  = r F sin , becomes  = L F  is torque r is equal to the lever arm L F is force Hinge: rotates r Direction of rotation  F

  17. Door Problem A standard door is 36 inches wide, with the doorknob located at 32 inches from the hinge (80 cm). Calculate the torque a person applies when he pushes on the doorknob at right angles to the door with a force of 110 N.  = 90o, so r = L

  18. Example 1:An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque. L • Extend line of action, draw, calculate L L= 12cm sin 600 = 10.4 cm t = (80 N)(0.104 m) = 8.31 N m

  19. Net Torque An object is in “Equilibrium” when: There is no net force acting on the object There is no net Torque In other words, the object is NOT experiencing linear accelerationor rotational acceleration.

  20. ?? 20 N ?? 20 N ?? 20 N What mass is needed for the levers to be in equilibrium? Weights are attached to 8 meter long levers at rest. Determine the unknown weights below

  21. What mass is needed for the levers to be in equilibrium? Upward force from the fulcrumproduces no torque (since r = 0) F2r2sinø2 = F1r1sinø1 (F2)(4)(sin90) = (20)(4)(sin90) F2 = 20 N … same as F1 r1 = 4 m r2 = 4 m F1 = 20 N F2 =??

  22. r1 = 4 m r2 = 2 m F1 = 20 N F2 =?? What mass is needed for the levers to be in equilibrium? F2r2sinø2 = F1r1sinø1 (F2)(2)(sin90) = (20)(4)(sin90) F2 = 40 N (force at the fulcrum is not shown)

  23. r1 = 3 m r2 = 2 m F1 = 20 N F2 =?? What mass is needed for the levers to be in equilibrium? F2r2sinø2 = F1r1sinø1 (F2)(2)(sin90) = (20)(3)(sin90) F2 = 30 N (force at the fulcrum is not shown)

  24. CM 20 N ?? More interesting problems(the pivot is not at the center of mass) Masses are attached to an 8 meter long lever at rest. The lever has a mass of 10 kg. Determine the unknown weight below.

  25. CM ?? 20 N Weight of lever More interesting problems(the pivot is not at the center of mass) Trick: gravity applies a torque “equivalent to” (the weight of the lever)(Rcm) tcm =(mg)(rcm) = (100 N)(2 m) = 200 Nm Masses are attached to an 8 meter long lever at rest. The lever has a mass of 10 kg.

  26. CM Rcm = 2 m R1 = 6 m R2 = 2 m Fcm = 100 N F1 = 20 N F2 = ?? Masses are attached to an 8 meter long lever at rest. The lever has a mass of 10 kg. Determine the unknown weight below. F2r2sinø2 = F1r1sinø1 + FcmRcmsinøcm (F2)(2)(sin90)=(20)(6)(sin90)+(100)(2)(sin90) F2 = 160 N

  27. bolt Diving board A 8 meter long diving board with a mass of 40 kg. a. Determine the downward force of the bolt. tcm = (392 N) 2 m = 784 Nm F1 r1 = F2 r2 + tcm The Pivot point is not at the center of mass

  28. bolt R1 = 2 Rcm = 2 Fcm = 392 N Fbolt = ? N Diving board A 8 meter long diving board with a mass of 40 kg. Determine the downward force of the bolt.(Balance Torques) F1 r1 = tcm F1 = 784Nm = 392 N 2m

  29. F = 784 N bolt Fbolt = 392 N Fcm = 392 N Diving board A 4 meter long diving board with a mass of 40 kg. b. Determine the upward force applied by the fulcrum.(Balance Forces)

  30. Remember: An object is in “Equilibrium” when: There is no net Torque b. There is no net force acting on the object

  31. Torque with two supports F2 F1 Fcm • Label all the forces • Choose a pivot point • Write the equation for net torques

  32. Torque with two supports F2 F1 Fcm Lcm T net = F1 L1 + Fcm L cm = F2 L2 cm L2 L1 Pivot point

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