PHYS_2014_Lecture_19

PHYS_2014_Lecture_19 - Fall 2010 Oklahoma State University...

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Unformatted text preview: Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 1 Torque is the rotational analog of force...it is the extension of force to rotational motion. For a force to cause rotation, three factors are important: 1. The magnitude of the force . 2. The distance from the axis of rotation to the point where is applied. 3. The angle at which is applied relative to . r a F a a F a F a F a r a r a sin r F rF = = a a a Lecture 19: Rotational Motion, Torque Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 2 sin C A B AB = = a a a The 2 nd type of vector multiplication A a B a C A B = a a a The cross product of two vectors, and , separated by an angle , is another vector, , that is perpendicular to the plane in which the first two vectors lie. A a B a The magnitude of can be found by: C A B = a a a C a Vector Cross Product The vector cross product is inherently three dimensional. Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 3 To find the direction of the vector that results from taking the cross product of and , we use the Right Hand Rule . A a B a C a Right Hand Rule The cross product does not obey the Commutative Law of Multiplication. A B B A A B B A = a a a a a a a a Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 4 In turning a nut, we apply 20 N of force to the end of a 25 cm wrench. What torque do we produce on the nut? r a F a a We get the maximum torque if = 90 , so we apply the force at that angle. sin 0.25m 20Nsin90 5N m = = = r rF r is frequently referred to as the lever or the lever arm . Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 5-x 1 x 2 x CM m 1 m 2 m 2 g m 1 g-x 1 x 2 Torque due to Gravity: Let us say we try to balance an object on a knife edge at a point that is not the center of mass. ( ) 1 2 1 1 1 2 2 2 2 2 1 1 g g x m g x m g x m x m g = + = = = Gravity will exert a torque on each point on an object. note that 1 is negative Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 19, Slide 6 In general, the total torque will be the sum of all the little torques acting on an object. ( ) g n n n n n CM g CM m x g m x Mx Mgx = = = = but Important Note: x CM is measured relative to the balance (pivot) point. Obviously the numerical value of x CM will be different if we try to balance the object at a different point. Fall 2010...
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This note was uploaded on 11/28/2011 for the course PSYCH 2014 taught by Professor Staff during the Fall '10 term at Oklahoma State.

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PHYS_2014_Lecture_19 - Fall 2010 Oklahoma State University...

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