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Copyright © 2012 Pearson Education Inc. Torque Physics 7C lecture 12 Thursday November 7, 8:00 AM – 9:20 AM Engineering Hall 1200

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Copyright © 2012 Pearson Education Inc. Loosen a bolt Which of the three equal-magnitude forces in the figure is most likely to loosen the bolt?

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Copyright © 2012 Pearson Education Inc. Loosen a bolt Which of the three equal-magnitude forces in the figure is most likely to loosen the bolt? torque τ is proportional to both force and distance.

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Copyright © 2012 Pearson Education Inc. Torque has its sign The line of action of a force is the line along which the force vector lies. The lever arm (or moment arm) for a force is the perpendicular distance from O to the line of action of the force (see figure). The torque of a force with respect to O is the product of the force and its lever arm.

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Copyright © 2012 Pearson Education Inc. Torque has its sign torque τ = r X F

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Copyright © 2012 Pearson Education Inc. The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. Which force produces the greatest torque about the point O (marked by the blue dot)? A. F 1 B. F 2 C. F 3 D. F 4 E. not enough information given to decide Q10.1 F1F1 F2F2 F3F3 F4F4 O

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Copyright © 2012 Pearson Education Inc. The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. Which force produces the greatest torque about the point O (marked by the blue dot)? A. F 1 B. F 2 C. F 3 D. F 4 E. not enough information given to decide A10.1 F1F1 F2F2 F3F3 F4F4 O

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Copyright © 2012 Pearson Education Inc. Calculate torque torque τ = r X F F = F x i + F y j r = x i + y j

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Copyright © 2012 Pearson Education Inc. Q10.4 What is the torque that this force applies about the origin? A. zero B. C. D. E. A forceacts on an object at a point located at the position

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Copyright © 2012 Pearson Education Inc. A10.4 What is the torque that this force applies about the origin? A forceacts on an object at a point located at the position A. zero B. C. D. E.

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Copyright © 2012 Pearson Education Inc. Torque as a vector Torque can be expressed as a vector using the vector product. how to find the direction of torque using a right hand rule.

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Copyright © 2012 Pearson Education Inc. Which of the four forces shown here produces a torque about O that is directed out of the plane of the drawing? A. F 1 B. F 2 C. F 3 D. F 4 E. more than one of these Q10.2 F1F1 F2F2 F3F3 F4F4 O

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Copyright © 2012 Pearson Education Inc. Which of the four forces shown here produces a torque about O that is directed out of the plane of the drawing? A. F 1 B. F 2 C. F 3 D. F 4 E. more than one of these A10.2 F1F1 F2F2 F3F3 F4F4 O

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Copyright © 2012 Pearson Education Inc. Applying a torque Calculate the torque

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Copyright © 2012 Pearson Education Inc. Applying a torque Calculate the torque

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Copyright © 2012 Pearson Education Inc. A plumber pushes straight down on the end of a long wrench as shown. What is the magnitude of the torque he applies about the pipe at lower right? A. (0.80 m)(900 N)sin 19° B. (0.80 m)(900 N)cos 19° C. (0.80 m)(900 N)tan 19° D. none of the above Q10.3

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Copyright © 2012 Pearson Education Inc. A. (0.80 m)(900 N)sin 19° B. (0.80 m)(900 N)cos 19° C. (0.80 m)(900 N)tan 19° D. none of the above A10.3 A plumber pushes straight down on the end of a long wrench as shown. What is the magnitude of the torque he applies about the pipe at lower right?

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Copyright © 2012 Pearson Education Inc. Torque and angular acceleration for a rigid body The rotational analog of Newton’s second law for a rigid body is z =I z.

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Copyright © 2012 Pearson Education Inc. Torque and angular acceleration for a rigid body Calculate angular accelaration

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Copyright © 2012 Pearson Education Inc. Torque and angular acceleration for a rigid body Calculate angular acceleration

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