An object of mass M = 3.00kg is attached to a spring with spring constant k = 82

Question

An object of mass M = 3.00kg is attached to a spring with spring constant k = 825N/m whose unstretched length is L = 0.190m , and whose far end is fixed to a shaft that is rotating with an angular speed of w= 5.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here.

1-Given the angular speed of w = 5.00radians/s , find the radius R(w) at which the mass rotates without moving toward or away from the origin.

2-Assume that, at a certain angular speed w2, the radius R becomes twice L. Find w 2.

Explanation / Answer

let the radius be x.so,

balancing the forces,

kx= mw^r

or 825*(R-0.19) = 3*5^2*(R)

or R=0.209 m

b) le tit be w.so,

3*w^2*(2*0.19)= 825*0.19)

or w=11.726 rad/s

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