An object of mass M = 5.00kg is attached to a spring with spring constant k = 88

Question

An object of mass M = 5.00kg is attached to a spring with spring constant k = 880N/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 ? = 4.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 4.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

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

Explanation / Answer

the angular momentum remains constant.

mvr = constant

here mis constant

vr = constant

r^2w =constant

r1^2w1=r2^2w2

w2=r1^2w1/r2^2

w2=(r1/r2)^2 * w1

w2=(1/2)^2 *w1

w2= 4/4 = 1 rad /s

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