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Class 17 - Center of Mass Reference Frames Physics 1301...

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1 Center of Mass, Reference Frames Physics 1301, Fall 2011: Class 17 Tuesday, October 11, 2011
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2 Objectives: Tuesday, October 11 Center of mass Reference frames
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3 Demonstrations
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Center of Mass The response of an extended body to forces and torques depends on how the mass is distributed in the body A useful (but not complete) description is to characterize the body in terms of 3 parameters Mass (does not depend on distance) Center of Mass (depends on distance) Moment of Inertia (depends of distance squared) 4
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Mass, CM, Moment of Inertia 5 M = m i i = 1 n M = ρ dV x cm = 1 M m i i = 1 n r i x cm = 1 M ρ r dV I = m i i = 1 n r i 2 I = ρ r 2 dV
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Example An object consists of three small spheres located at the centers of an equilateral triangle 10.0 cm on a side connected by very light rods. Each sphere has a mass of 1.00 kg. One of the spheres is located at the origin. What are the coordinates of the cm? 6 (0,0) (?,?) (?,?) (a) (0,0) (b) (10,0) (c) (10,10) (d) (5, 8.66) (e) (5,2.89)
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Example An object consists of three small spheres located at the centers of an equilateral triangle 10.0 cm on a side connected by very light rods. Each sphere has a
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