An object of mass = 4.00 is attached to a spring with spring constant = 176 whos

Question

An object of mass = 4.00 is attached to a spring with spring constant = 176 whose unstretched length is = 0.120 , and whose far end is fixed to a shaft that is rotating with an angular speed of = 2.00 . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 as shown. (Intro 1 figure) When solving this problem use an inertial coordinate system, as drawn here. (Intro 2 figure)

Assume that, at a certain angular speed , the radius becomes twice . Find .
Express your answer in radians per second.

Explanation / Answer

initial radius = 0.12;
double radius = 0.12*2 = 0.24 ;

so change in length of spring =0.12;
so at double radius, F = mr2 = kx;

4*0.24*2 = 176*0.12;

so = 4.69rad/sec

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