Torque

Think of these! ,[object Object],[object Object],[object Object]

OUR TARGET ,[object Object],[object Object],[object Object]

Let’s recall: ,[object Object]

The First Condition of Equilibrium ,[object Object],[object Object]

F F N S F F Does equilibrium exist if you exert a pair of equal opposing forces F to the right and to the left of the lug wrench? Situation 1

F F E W F F If the same two forces are applied as shown in the figure, does equilibrium exist? Situation 2

Questions ,[object Object],[object Object],[object Object]

N S F F E W F F VECTOR DIAGRAMS SITUATION 1 SITUATION 2 How would you compare the vector sum of the forces in the two situations?

N S F F N W F F VECTOR DIAGRAMS SITUATION 1 SITUATION 2 How would you compare the effect of the pair of equal forces applied on the lug wrench in the two situations?

N S F F N W F F VECTOR DIAGRAMS SITUATION 1 SITUATION 2 What is the difference in the application of the two equal forces in situations 1 and 2?

THE LINE OF ACTION ,[object Object],F F F F S Λ

THE MOMENT ARM ,[object Object],W Axis of rotation Line of action

THE MOMENT ARM ,[object Object],F Line of action r = L sin θ Axis of rotation Length L

[object Object],[object Object]

A B C F F F Given three unbalanced forces A, B and C 1. What is the moment arm of A? B? C? 2. How would you compare the rotational effect of A, B and C? 3. Which of the three unbalanced forces A, B, and C is the most effective in producing rotational motion? Why? Least effective? Why?

A B C F F F 1. What is the moment arm of A? B? C? 2. How would you compare the rotational effect of A, B and C? 3. Which of the three unbalanced forces A, B, and C is the most effective in producing rotational motion? Why? Least effective? Why?

TORQUE is the tendency to produce a change in rotational motion. It is also called moment of force.

Mathematically: ,[object Object],Where: τ (tau) = torque( in Newton-meter, N-m or pound-foot, lb-ft) F = force (in Newton, N or pound, lb) r = moment arm (in meter, m or foot, ft) Torque = Force x moment arm

Sign Convention ,[object Object],[object Object],[object Object]

F F (-) (+) (+) (-) F Clockwise torque Counterclockwise torque

Illustrative Example ,[object Object],A F B 2 m 3 m

Solution ,[object Object],A F B 2 m 3 m The moment arm about point B is the perpendicular distance from point B to the line of action of the force F

Illustrative Example ,[object Object],A F B 2 m 3 m 30 °

2. Solution ,[object Object],A F B 2 m 3 m 30 ° Its magnitude is : r = L sin 30 ° = 2m (0.500) = 1.0 m

3. Solution ,[object Object],A F B 2 m 3 m 30 ° Its magnitude is : r = L sin 30 ° = 3m (0.500) = 1.5 m

Illustrative Examples ,[object Object],A F B 2 m 3 m 30 °

4. Solution A F B 2 m 3 m 30 ° Since r A = 1.0 m and F = 100 N T A = Fr A = 100 N (1.0 m) = 100N-m r = 1.0 m -

4. Solution Since r B = 1.5 m and F = 100 N T B = Fr B = 100 N (1.5 m) = 150N-m A F B 2 m 3 m 30 ° r = 1.5 m

Sum it up. ,[object Object],[object Object]

Check your understanding. ,[object Object],[object Object]

Which of the following will produce the greatest torque? D= 1000 N C=600 N A= 1000 N B=150 N 2.0 m 3.5 m 2.5 m 8.0 m

Which of the following will produce the greatest torque? D= 1000 N C=600 N A= 1000 N B=450 N 2.0 m 3.5 m 2.5 m 8.0 m 20 ° 60 ° T = 1000N (2.0m)sin60 ° = 1732 N-m T = 450N (5.50 m) = 2475 N-m T = 600N (5.50m)sin 20° = 1129 N-m T = 1000N (0.0m) = 0

Assignment ,[object Object],[object Object],[object Object]

[object Object],If F 1 = 10 N, and is at a distance of 0.25 m from O, where Θ 1 = 30 ° F 2 = 7.0 N, acting perpendicular to the object, at a distance of 1.25 m from O F 3 = 12 N, is 0.60 m from O, and acts at Θ 3 = 40 ° from the horizontal Find the total (net) torque on the object.

[object Object],Did MCS ever extend a helping hand to you when you are in need? At your end, how do you support the school in helping others in need? Think about this.

Figure 1 object with several torques. The net total torque on the object is: A . -1.7 N m B . -15.8 N m C . -6.6 N m D . 18 N m

Solution ,[object Object],[object Object],[object Object]

Calculate for moment arm and torque

Torque

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