Spring force:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{k}}{\mathbf{x}}}$

Centripetal force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{m}}{\mathbf{r}}{{\mathbf{\omega}}}^{{\mathbf{2}}}}$

**(a)**

ΣF = mRω^{2} - kx = 0

mRω^{2} = kx

mRω^{2} = k(R - L)

An object of mass *M* = 5.00 kg is attached to a spring with spring constant *k* = 220 N/m whose unstretched length is *L* = 0.180 m , and whose far end is fixed to a shaft that is rotating with an angular speed of *ω* = 2.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/s

Given the angular speed of *ω* = 2.00 radians/s , find the radius *R*(*ω*) at which the mass rotates without moving toward or away from the origin, in meters.

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