Lecture_23web_2007

Lecture_23web_2007 - Quiet please ladies and gentlemen The...

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Quiet please ladies and gentlemen The lecture is about to begin n
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Centre of mass in a nutshell 1 1 n i i i cm n i i m x x m = = =
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Moving objects
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A system of moving particles ( 29 1 2 1 1 2 2 cm x m m m x m x + = + ( 29 1 1 2 2 1 2 cm m x m x x m m + = + ( 29 1 2 1 2 1 2 cm x x x m m m m t t t ∆ ∆ ∆ + = + ∆ ∆ ∆ ( 29 1 2 1 1 2 2 cm m m m m υ + = + 1 1 2 2 cm M m m = + 1 2 M m m = + Total momentum of the system of particles is equivalent to the total mass of the system times the velocity of its centre of mass
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2 0 i = υ 1 i υ 1 0 f = υ 2 f υ A system of moving particles In the previous example the particles made a ridged object but this need not be the case constant cm = υ C of m
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C of M in 2D 1 m g 2 m g 3 m g x y 1 x cm x 2 x 3 x ( 29 1 1 2 2 3 3 1 2 3 cm m x m x m x x m m m + + = + +
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C of M in 2D 1 m g 2 m g 3 m g x y 1 y cm y 2 y 3 y ( 29 1 1 2 2 3 3 1 2 3 cm m y m y m y y m m m + + = + +
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C of M in 2D 1 m g 2 m g 3 m g x y cm y cm x C of m
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cm y cm x CM x y 0 Centre of mass of a regular object and uniform density A square b / 2 b
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cm y cm x CM x y 0 Centre of mass of a regular object and uniform density A rectangle b / 2 b h / 2 h
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cm y cm x CM x y 0 Centre of mass of a regular object and uniform density A circle r
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Lecture_23web_2007 - Quiet please ladies and gentlemen The...

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