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**Torque and Equilibrium**

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Torque What exactly is torque in normal English? Rotational effect of force. Tells how effective force is at twisting or rotating an object. tnet = I α t = +- r Fperpendicular = r F sin q Units N m Sign, CCW rotation is (usually) positive Why is there a sine theta in the Torque equation!?!!??! 07

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Question The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which of the cases is the torque on the nut the biggest? A. Case 1 B. Case 2 C. Case 3 10

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Question 2 The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which of the cases is the torque on the nut the smallest? A. Case 1 B. Case 2 C. Case 3 12

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Torque Example A person raises one leg to an angle of 30 degrees. An ankle weight (89 N) attached a distance of 0.84 m from her hip. What is to torque due to this weight? If she raises her leg higher, the torque due to the weight will A) Increase B) Same C) Decrease 30 F=89 N r = 0.84 m 17

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Equilibrium A rod is lying on a table and has two equal but opposite forces acting on it, one on each end. What is the net force on the rod? A) Up B) Down C) Zero Will the rod move? A) Yes B) No y x F F 21

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**Equilibrium Conditions for Equilibrium**

S F = Translational EQ (Center of Mass) S t = Rotational EQ Can choose any axis of rotation…. Choose Wisely! Steel from podium 25

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Example: Equilibrium A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it? 9.8 N 19.6 N 50 cm d Steel from podium 25

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Question The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight? 1. The person on the left is supporting the greatest weight 2. The person on the right is supporting the greatest weight 3. They are supporting the same weight 33

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Example: hanging beam A 40kg uniform beam is being supported by two ropes. What is the tension in each rope? 2m 40kg 3m

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Example: painter A painter of mass 50kg uses two supports and a plank of mass 20kg as a platform to paint his house.How far to the right of support B can the painter stand before the plank tips? A B 1 meter 3 meter 20kg Painter homework problem. Get demo here have man stand at several places calculate force on each support. Right above support, middle Just before board tips, force from A becomes zero 47

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Example: continued A B 1 meter 3 meter 20kg

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Example: falling beam If the right rope breaks, what is the initial angular acceleration of the beam? 2m 40kg 3m

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Example: Rolling An hoop with mass M, radius R, and moment of inertia I = MR2 rolls without slipping down a plane inclined at an angle = 30o with respect to horizontal. What is its acceleration? Consider CM motion and rotation about the CM separately when solving this problem I M R 29

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Rolling... Static friction f causes rolling. It is an unknown, so we must solve for it. First consider the free body diagram of the object and use In the x direction Now consider rotation about the CM and use = I M y x f Mg R 33

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**Rolling... We have two equations: We can combine these to eliminate f:**

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**Summary Torque = Force that causes rotation Equilibrium tnet = I α**

t = F r sin q Work done by torque W = t q Equilibrium S F = 0 S t = 0 Can choose any axis. 50

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