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Stochastic13
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Homework Statement
An object is moving counterclockwise in a circle of
radius r at constant speed v. The center of the cir-
cle is at the origin of rectangular coordinates (x, y),
and at t = 0 the particle is at (r, 0). If the “angular
frequency” is given by ω = v/r, show that
[tex]\ddot{}x[/tex] + ω2 r = 0 and y'' + ω2 r = 0
Homework Equations
ω = v/r
The Attempt at a Solution
If particle is at (r,0) then r = x
we know: ar = v2/r = ω2 r
since velocity is constant ar = 0
so x'' has to equal 0 thus x'' + ω2 r = 0
the same argument can be applied to y'' + ω2 r = 0
proving the second statement.
Is this correct? Is there a better way of showing the two statements are true?
Sorry for using '' instead of like I did on the first x + ωr = 0 since they rarely work
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