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Understanding Torque

Understanding Torque. 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. Definition of Torque.

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Understanding Torque

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  1. Understanding Torque 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.

  2. Definition of Torque Torque is defined as the tendency to produce a change in rotational motion. Examples:

  3. 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.

  4. 6 cm 40 N Units for Torque Torque is proportional to the magnitude of F and to the distance r from the axis. Thus, a tentative formula might be: t = Fr Units: Nm or lbft t = (40 N)(0.60 m) = 24.0 Nm, cw t = 24.0 Nm, cw

  5. 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.

  6. 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

  7. 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

  8. F1 F2 F3 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. r r r

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

  10. 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. r = 12cm sin 600 = 10.4 cm t = (80 N)(0.104 m) = 8.31 N m

  11. positive Alternate:An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque. 12 cm Resolve 80-N force into components as shown. Note from figure: rx = 0 and ry = 12 cm t = 8.31 N m as before t = (69.3 N)(0.12 m)

  12. Calculating Resultant Torque • Read, draw, and label a rough figure. • Draw free-body diagram showing all forces, distances, and axis of rotation. • Extend lines of action for each force. • Calculate moment arms if necessary. • Calculate torques due to EACH individual force affixing proper sign. CCW (+) and CW (-). • Resultant torque is sum of individual torques.

  13. negative 20 N 30 N 300 300 2 m 6 m A 4 m 40 N Example 2:Find resultant torque about axis A for the arrangement shown below: Find t due to each force. Consider 20-N force first: r The torque about A is clockwise and negative. r = (4 m) sin 300 = 2.00 m t = Fr = (20 N)(2 m) = 40 N m, cw t20 = -40 N m

  14. r 20 N 30 N negative 300 300 2 m 6 m A 4 m 40 N Example 2 (Cont.):Next we find torque due to 30-N force about same axis A. Find t due to each force. Consider 30-N force next. The torque about A is clockwise and negative. r = (8 m) sin 300 = 4.00 m t = Fr = (30 N)(4 m) = 120 N m, cw t30 = -120N m

  15. positive 20 N 30 N r 300 300 2 m 6 m A 4 m 40 N Example 2 (Cont.):Finally, we consider the torque due to the 40-N force. Find t due to each force. Consider 40-N force next: The torque about A is CCW and positive. r = (2 m) sin 900 = 2.00 m t = Fr = (40 N)(2 m) = 80 N m, ccw t40 = +80N m

  16. 20 N 30 N 300 300 2 m 6 m A 4 m 40 N Example 2 (Conclusion):Find resultant torque about axis A for the arrangement shown below: Resultant torque is the sum of individual torques. tR = t20 + t20 + t20 = -40 N m -120 N m + 80 N m tR = - 80N m Clockwise

  17. This concludes the general treatment of torque. Part II details the use of the vector product in calculating resultant torque. Check with your instructor before studying this section. Part II: Torque and the Cross Product or Vector Product. Optional Discussion

  18. F Sin q F Torque q The Vector Product Torque can also be found by using the vector product of force F and position vector r. For example, consider the figure below. The effect of the force F at angle q (torque) is to advance the bolt out of the page. r Magnitude: (FSinq)r Direction = Out of page (+).

  19. F Sin q q r Definition of a Vector Product The magnitudeof the vector (cross) product of two vectors A and B is defined as follows: AxB= l A l l B l Sin q In our example, the cross product of F and r is: F xr = l F l l r l Sin q Magnitude only In effect, this becomes simply: F (F Sin) r or F (r Sinq)

  20. 600 6 in. r xF = 62.4 lb in. r xF = 62.4 lb in. Torque 6 in. 600 Torque 12 lb Example:Find the magnitude of the cross product of the vectors r and F drawn below: 12 lb r xF = l r l l F l Sin q r xF = (6 in.)(12 lb) Sin 600 r x F = l r l l F l Sin q r xF= (6 in.)(12 lb) Sin 1200 Explain difference.Also, what aboutFx r?

  21. C B A B A -C Direction of the Vector Product. The direction of a vector product is determined by the right hand rule. A x B = C (up) Curl fingers of right hand in direction of cross pro-duct (A to B) or (B to A). Thumb will point in the direction of product C. B x A = -C (Down) What is direction of A x C?

  22. 10 lb 500 r xF = 38.3 lb in. 6 in. Torque F r Out Example:What are the magnitude and direction of the cross product, r x F? r xF = l r l l F l Sin q r xF = (6 in.)(10 lb) Sin 500 Magnitude Direction by right hand rule: Out of paper (thumb) or +k r xF = (38.3 lb in.) k What are magnitude and direction of F x r?

  23. Torque = force x moment arm t = Fr Summary Torqueis the product of a force and its moment arm as defined below: The moment arm of a force is the perpendicular distance from the line of action of a force to the axis of rotation. The line of action of a force is an imaginary line of indefinite length drawn along the direction of the force.

  24. Summary: Resultant Torque • Read, draw, and label a rough figure. • Draw free-body diagram showing all forces, distances, and axis of rotation. • Extend lines of action for each force. • Calculate moment arms if necessary. • Calculate torques due to EACH individual force affixing proper sign. CCW (+) and CW (-). • Resultant torque is sum of individual torques.

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