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serverxeon
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Homework Statement
an ball of mass m is connected by a string with spring constant k, to a rotating shaft.
Find a relation between the radius of the circle, and the angular frequency.
Homework Equations
The Attempt at a Solution
Let:
Natural length of spring = x0
Extension of spring = x
Radius of circle = r = x + x0
Centripetal force = Force due to spring
mrω2 = kx = k(r-x0)
Make r the subject,
mrω2 = kr-kx0
kx0=kr-mrω2
kx0=r(k-mω2)
r=[itex]\frac{kx_{0}}{k-m\omega^{2}}[/itex]
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The expression indicates that there is an asymptote when [itex]\omega=\sqrt{\frac{k}{m}}[/itex]
Does this means the rotation can never hit this angular velocity?