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lec25_review30 - Physics I Review 3 Review Notes Exam 3 Ch...

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R3-1 Physics I Review 3 Review Notes - Exam 3 Ch 12, 13, 15, 16, 17, 21
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26-2 Equilibrium for Rigid Objects When dealing with objects that have finite size, we specify external forces and external torques. Equilibrium: constant ( ) constant any coordinate system any axi ( ) so, 0 0 s ext ext P L F τ = = = =
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Center of Gravity When calculating torque due to gravity we can use the center-of-mass, renamed center-of-gravity. dm=(M/L)dx 0 2 0 ( ) | What is the direction of | | | | 2 2 2 | ( ) ? ext cm grav L ext e grav L ext xt xgM d xg dm dx L xgM d dx L x x gM LgM L M L Mg g τ τ τ τ τ τ = = ÷ = = ÷ = = = ÷ =
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R3-4 Newton’s Law of Universal Gravitation r m m G F 2 2 1 = The meaning of each term: F : Gravitational force on object 1 from object 2. G : Universal gravitational constant = 6.673 x 10 –11 N m 2 /kg 2 . 1 m : Mass of object 1. 2 m : Mass of object 2. 2 r : Center distance from object 1 to object 2, squared. : Unit vector from object 1 to object 2.
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R3-5 If Gravity Varies As 1/r 2 , Where Does g = 9.8 m/s 2 Fit In? Consider the force on an object near the surface of the earth. (Assume the earth is a sphere and ignore rotation effects.) R = radius of the earth. M = mass of the earth. m = mass of the object. g m R M G m R M m G F 2 2 = = = (What is the direction?) g = 9.8 m/s 2 only seems constant because we don’t go very far from the surface of the earth.
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Gravity is a Conservative Force Since the force goes to zero at infinite distance, we set the gravitational potential energy to zero there also (it's the only unique point): 2 ( ) ( ) ( ) ( ) grav grav grav R R grav R U R U U R
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