Spinning Mass on a Spring An object of mass Mis attached to a spring with spring

Question

Spinning Mass on a Spring An object of mass Mis attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with angular speed w Neglect gravity and assume that the mass rotates with angular speed was shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. ure 2 gure 1 Part A Given the angular speed w. find the radius R(w) at which the mass rotates without moving toward or away from the origin. Express the radius in terms of k, L, M, and w. kL k-Mi Submit Hints My Answer Give Up Review Part Correct Part B Assume that, at a certain angular speed w2. the radius Rbecomes twice L Find w2 Answer in terms of kand M. 2M Submit Hints My Answers Give Up Review Pa Correct Part C You probably have noticed that, as you increasew, th will be a value. wcrit, for which R(w) goes to infinity. Find worit. ere Answer in terms of kand M. Wcrit Submit Hints My Answers Give Up Review Part Part D This question will be shown after you complete previous

Explanation / Answer

the answer for part c is w_crit = sqrt(k/M)

proof:

from part A, R(W)=Kl/K-mw^2

as we know that W increases,denominator equals zero

therefore,   K-MWcrit^2=0

thus Wcrit=sqrt(K/M)

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